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SOLID ROCKET
PROPULSION TECHNOLOGY
Edited by
Alain Davenas
ancien eleve de I'Ecole Polytechnique
Technology and Research Director, SNPE, France
PERGAMON PRESS
OXFORD • NEW YORK • SEOUL • TOKYO
U K. Pergamon Press Ltd, Headington Hill Hall,
Oxford 0X3 OBW, England
U.S.A. Pergamon Press, Inc, 660 White Plains Road, Tarry-
town, NY 10591-5153, U.S.A.
KOREA Pergamon Press Korea, Room 613 Hanaro Building,
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Korea
JAPAN Pergamon Press Japan, Tsunashima Building Annex,
3-20-1 2 Yushima, Bunkyo-ku, Tokyo 1 1 3, Japan
English translation Copyright© 1993 Pergamon Press
Ltd.
Translation of: Technologie des propergols solides.
Copyright © Soci6t6 Nationale des Poudres et Explo-
sifs, and Masson, Paris, 1988
AH Rights Reserved . No part of this publication may be
reproduced , stored in a retrieval system or transmitted
in any form or by any means: electronic , electrostatic,
magnetic tape , mechanical, photocopying, recording
or otherwise, without permission in writing from the
copyright holders
First English edition 1993
Library of Congress Cataloging-in-Publication Data
Technologie des propergols solides. English.
Solid rocket propulsion technology/edited by Alain
Davenas.
p. cm.
Translation of: Technologie des propergols solides.
Includes bibliographical references.
1. Solid propellant rockets. I. Davenas, Alain. II. Title.
TL783.3.T431 3 1991 662'.26— dc20 90-25612
British Library Cataloguing in Publication Data
Solid rocket propulsion technology.
1. Aerospace vehicles. Engines
I. Davenas, Alain
629.1
ISBN 0-08-040999-7
Printed in Great Britain by The Bath Press, Avon
Foreword
This book is a translation, with some slight adaptations, of Technologie des
propergols solides , published in French in 1989.
There are few books on solid propellants and their use in rocket propul-
sion, and few of these present a comprehensive review of the field.
There are many reasons for this. For the most part, applications of this
technology, with the exception of fireworks displays, have been limited to the
fields of advanced armament and space activities. Therefore, most of it has
been protected by industrial or military security classifications. It was thus
necessary to wait for the moment when a significant quantity of data would
be disclosed through open literature or patents.
These restrictions on the free flow of information led to different designs
and methods in different countries. In France, for instance, there has been
intensive use of trimmed axisymmetric grain designs with high loading
fractions which have not been developed in any other countries, and for
which the design and production methods were protected by a “secret”
classification for a long time. In the USSR a very specific composite
propellant formulation has been used in a family of missiles, with a binder
that uses a derivative of a terpenic resin found only in the Ural forests of the
USSR.
The technology of propellants is, like other technology, subject to the
influence of fashionable trends. In France today, for example, Finocyl grain
designs are currently popular. The main reason for this is probably that
Finocyl geometries are very adaptable to various flow rate or thrust
requirements. There are, however, cases where a simple star-shaped design
would have satisfied the main requirements, and also offered some better
secondary characteristics.
While the original objective was to present, to the extent possible, a
universal body of knowledge, factors such as restricted information flow,
specific industrial developments in various countries and fashionable trends
have sometimes made this difficult. Readers may therefore find a French
flavor to some of the chapters.
As already stated, we tried to cover all aspects of the field, and consequently
this is a long book. We had to be as concise as possible on each subject;
therefore we often refer the reader to what we feel is essential material for
additional information. One original intention was that each chapter should
be readable independent of the others, implying a great amount of redun-
Foreword
xii
dancy. Because of space limitations we discovered that this could not be
done. Therefore, some chapters refer to other chapters. This practice was,
however, kept to a minimum, and we used a traditional approach: each
chapter uses concepts already developed in previous chapters.
After a first chapter reviewing the fundamentals of rocket propulsion, the
second chapter develops all the descriptive aspects. The second chapter is
recommended to anyone who is interested only in reading about one of the
more specialized subjects found in later chapters. The subsequent chapters
present the specific design methods and the theoretical physics underlying
them. These are chapters where, after the fundamental mechanisms involved
in the working of propulsion systems are presented, the rules of the art and
specialized engineering methods are then deduced.
The last part of the book deals with the industrial production of the most
important motor component: the propellant, and the inert materials, such as
thermal insulations and bonding materials.
Some subjects of common interest to different chapters are covered in only
one of them. Hence, processes used to manufacture composite propellants,
used for composite double-base propellants (Chapter 11), are covered in
Chapter 10. Non-destructive testing techniques used for every type of grain
are also found in Chapter 10. Some mechanisms for the transition from
deflagration to detonation are described in Chapter 1 1. The decomposition of
nitrate esters and critical dimensions for cracking by internal pressure are
discussed only in Chapter 9; vulnerability issues are discussed in Chapter 8,
etc.
All authors who contributed to this work belong to the same company:
Societe Nationale des Poudres et Explosifs — SNPE. The reason for this is
quite simple. SNPE originated from a famous official French governmental
organization: the “Service des Poudres”. For several centuries this organiza-
tion held the monopoly in France for the production of “explosive sub-
stances” (substances that can deflagrate or detonate). During the 19th
century and the first part of the 20th century it was one of the great French
chemical groups where fundamental research in the field of physical chem-
istry was most advanced. SNPE has kept the mandate, for reasons of national
interest, to develop all types of products for propulsion applications and for
all basic research programs in this area, differing from most other countries,
where companies often specialized in only one family of products.
Daniel Quentin had the original idea for this project, and stimulated the
first drafts. The requirements of his professional activities took him very far
away from France, making it impossible for him to participate directly in
later drafts. Even though there is now little left from the voluminous first
drafts, these had the great merit of resulting in internal documents on each
subject that are proving to be extremely valuable for our company.
I was assisted, for the French version of this book, by a very conscientious
editorial committee that included Claude Grosmaire, Roland Lucas and
Foreword
xiii
Bernard Zeller, later replaced — again because of the press of other profes-
sional duties — by Rene Couturier.
The French edition of this book was published by Masson, Paris, at the
beginning of 1989 with the usual high standards of this publisher. It found
quickly a significant audience (relatively speaking!) but its diffusion would
nowadays stay essentially limited to French-speaking countries.
The publication of an English version was considered at an early stage.
Pergamon Press, with its dynamic policy, agreed to publish it despite the
limited audience of this specialized subject. We asked Mrs Anne Baron,
Daniel Quentin’s assistant, to make a first draft of translation. This draft was
then reviewed by the authors with the help of their knowledge of the
vocabulary of their technical field. Then we asked some English-speaking
colleagues, knowledgeable in the field, to check our translation. We wish to
express all our gratitude to Miss Carol Jones (Chapter 13), Professor Beddini
(4) and to Tom Boggs (9), John Consaga (11), Ron Derr (3), Geoffrey Evans
(9), Ray Feist (2), Joseph Hildreth (1), Frank Roberto (8, 10, 14), Bert Sobers
(12), Frank Tse (6) and Andy Victor (5).
Some of the problems we encountered during the translation were due to
the fact that some concepts that are represented by one word in one language
needed a long sentence for their translation — and this to my surprise is true
both ways (for instance “autoserrage” for “burning area to port area ratio”
or “indice structural” for “ratio of inert mass to propellant mass for a given
motor”, etc.). Another difficulty was that terminology has sometimes still to
be standardized even if some progress is being made in this area (for example
in low visible signature propellants, hazards classification, etc.). This is
particularly true for propellant formulations. We have developed in French a
specific terminology to name propellants according to their main compo-
nents, which is compact, efficient and (of course!) Cartesian. It was used for
the French version but there is no English equivalent so we had to decide, for
the English vocabulary, somewhat arbitrarily. Some traces of the French
names may be found in some chapters. In case of possible ambiguities we
have made a special presentation, in an addendum, of the decisions we have
taken to name propellants in English, and the rules of French terminology.
Since the French edition was published, at the beginning of 1989, there has
not been much important evolution in solid propulsion technology, so the
changes made are quite limited.
Some developments on program management were suppressed in Chapter
8 because they were very specific to the French organization. A small
addition was made in Chapter 12 on integral boosters that were briefly
mentioned in the French edition, and in Chapter 7 on XDT (delayed
detonation through shock). Some developments related to clean propellants
for future space boosters and continuous-mixing processes of composite
XIV
Foreword
propellant, which may become important in the near future were added to
Chapter 14. Some “fresh” references were added to some chapters.
On behalf of myself and my co-authors I would like to record our gratitude
to our colleagues at SNPE, whose names do not always appear, for their
generous cooperation in the preparation of this book. We would also like to
thank all those who have provided illustrations.
Finally I would like to thank my wife Cathy for her patience and
understanding during the summers of 1987 and 1988 (French version) and
1989 (English version) while I was assuming my editorial duty, and to thank
my supervisor, Pierre Dumas, who encouraged me with this work, even when
business was brisk, also all our French, British and American colleagues and
friends who helped us in this task.
Alain Davenas
Note on International
Nomenclature for Solid
Propellant Compositions
Terminology for propellants has still to be standardized. Many equivalent
names for the same propellant can be found in the literature (or in this book);
besides that the French have developed a specific terminology for composite
and high-energy propellants which is described in Chapter 2, Section 3.2.1.
This is probably due to the fact that authors sometimes refer to the chemical
composition, sometimes to the production process and sometimes to some
functional characteristics such as smoke or mechanical properties (e.g.
elastomeric modified double-base).
Homogeneous propellants are also called (surprisingly) double-base pro-
pellants (based on nitrocellulose and a nitric ester). The two main types are
extruded double-base or EDB (in French SD for “sans dissolvant”, meaning
without solvent) and cast double-base or CDB (in French Epictete!). When
energetic solids are introduced into this propellant it becomes a CMDB, for
composite modified double-base. This name is used only for cast propellants
even if some EDBs can contain oxidizers or energetic solids. Elastomeric
modified cast double-base or EMCDB propellants have been developed.
They are cast double-base propellants in which an elastomeric binder has
been added to the double-base. They can involve the addition of energetic
solids. In French, since it is a composite propellant, the rules for nomencla-
ture apply: these propellants are nitrargols (generic term). If they contain AP
they will become nitralites. If they contain HMX they will be nitramites, etc.
These propellants will be minimum smoke propellants if their formula
contains only or mostly C, H, O, N.
In English composite propellants are generally named according to their
binder, e.g. HTPB or polyurethane propellants, etc., which of course leaves
ambiguity except for the fact that most industrial composite propellants use
AP for oxidizer, and this is generally implied. The presence of a solid fuel is
less clear, since more and more “reduced smoke” propellants, i.e. without
metallic fuel, are used in practical applications. In French the names will vary
according to the main ingredients of the composition. For instance a
composite propellant based on polybutadiene, AP, A1 will be a butalane.
Without A1 it will be a butalite, etc.
xv
xvi Nomenclature for Solid Propellant Compositions
So-called high-energy propellants are generally composite propellants with
an energetic binder. The most typical use a nitroglycerine plasticized binder
and are called XLDB for crosslinked double-base even if there is almost no
nitrocellulose in the binder. In French they are nitrargols (nitra for the
binder). Minimum smoke XLDB based on HMX, for instance, are nitramites.
The terms “minimum smoke” and “reduced smoke” are themselves not
sufficient to differentiate propellants clearly. A working group of AGARD is
now trying to define more clearly the level of smoke, in order to be able to
compare different propellants made in different countries or organizations.
The idea is to characterize the level of primary and the level of secondary
smoke of any propellant. In order to be independent of the method and
hardware used to measure optical transmission, the classification will be
made by reference to two given defined propellants, and the level of smoke
will be considered as higher than or lower than . . .
CHAPTER 1
Propulsion Elements for Solid
Rocket Motors
ROLAND LUCAS
1. Principles of Propulsion
1.1. INTRODUCTION
Rocket launches have become a familiar spectacle. Newspapers, movies
and television frequently show us the images of the first moments of lift-off.
Impressed by the large quantity of gases released at the lift-off of the rocket, a
knowledgeable spectator will deduce the relationship between cause and
effect. As a perceptive observer he will have in fact discovered the principle of
propulsion, which links reaction force to the ejection of a mass.
Expressed by an equation and applied to rockets, this principle is:
F = q • Ve
where F is the reaction force which we call thrust, q is the gas mass flow rate
and Ve the exhaust velocity of the gases.
Following his logical line of reasoning, the observer will then wonder
about the origin of such a volume of gas ensuring for many seconds the
propulsion of the rocket. If his creative mind leads him to think of the
burning of a solid mass, on board the rocket, he will then have imagined the
concept of solid fuel rockets.
1.2. MAIN COMPONENTS OF A ROCKET MOTOR
The rocket motor (Fig. 1) is designed to ensure the combustion under
pressure of the propellant grain it contains. The resulting gases are expanded
through the nozzle, whose function is to convert this pressure into supersonic
exhaust.
As a rule, such a rocket motor has five major components.
1
2
Roland Lucas
Inhibitor
Generator
Generator
igniter
Gas generator Main propellant grain Nozzle
for rotation Thermal
insulation of case
Propellant grain
A
Case
Nozzle
insulator
Section A - A'
Liner
PT AV Ignition
pyrotechnic
chain
Fig. 1.1. Typical rocket motor.
1.2.1. The case
Made either from metal (high-resistance steels) or from composite mater-
ials by filament winding (glass, kevlar, carbon), the case must be capable of
withstanding the internal pressure resulting from the motor operation,
approximately 3-25 MPa, with a sufficient safety coefficient, usually of the
order of 1 .4.
1.2. 7. 7. Ballistic missiles and space launchers
For ballistic missiles and space launchers, special industrial resources have
been developed to manufacture cases with an internal volume of up to about
10 cubic meters.
(a) Metal cases
Several types of steel are used for the metal cases (such as AMS 6487 or
AMS 6520) whose main characteristics are their great mechanical strength,
usually greater than 1000 MPa, and the ease with which they can be shaped.
For the cylindrical body, two manufacturing methods are used:
• wrapping-welding of long steel sheets, requiring longitudinal welding;
• flow turning of rough forgings, avoiding the drawback of welding and
offering the possibility of progressive thicknesses.
Propulsion Elements for Solid Rocket Motors
3
The technique used for the production of the end closures of the cases
involves the machining of solid thermal press forgings. Consequently grooves
for handling, and for the interfacing between the various stages, can be
obtained from a solid steel block. The end closures and cylindrical body are
welded together. The additional manufacturing cycles involve various ther-
mal treatments (hardening, tempering), finish machining, surface treatments
(anti-corrosion) and a pressurization test above the maximum expected
operating pressure (over-test coefficient of the order of 1.15).
Quality control testing is performed at every stage of the manufacture,
including tests of metal properties, X-ray and ultrasonic testing [1].
(b) Composite material cases
The so-called filament-wound cases use composite materials spun into
filaments (glass, kevlar, carbon) and a matrix consisting of thermosetting
resin of a polyester, epoxide or polyamide type. An overview of these
composite materials for propulsion application is shown in ref. [2].
Based on the internal pressure requirements during operation, the design
analysis of a case of this type is done in two stages: a preliminary design
phase, followed by a testing phase [3]. The first phase is based on the
principle that the case has rigidity only in the direction of the filaments.
Geometry, corresponding thicknesses, as well as the winding law ensuring the
fiber stability requirement (elimination of the risk of slippage during the
winding) can be rapidly determined. The second stage uses the computational
methods with finite elements by considering the material as a homogeneous
orthotropic solid, and enables verification of the structural integrity of the
whole.
Once the design has been completed, and the manufacturing parameters
determined, manufacture of the case may begin. The fibers, impregnated with
resin, are wound on a mandrel shaped as required with the help of a special
lathe. The mandrel, an agglomerate of sand, or a metallic piece fitting, is first
coated with the thermal insulation intended for the case and is equipped with
metal polar bosses at both ends. These metal bosses help strengthen the
forward and aft openings and provide the connection with the other
components, such as the ignition system and the nozzle. There are two
winding methods: the wet process which involves continuous impregnation
during manufacture or the dry process, which uses previously impregnated
fibers. Two successive types of filament winding are necessary:
• the first filament winding is a succession of loops tangential to the two
openings: this is “helix” or “polar” winding, designed to cover the domes
and the case;
• the second filament winding covers only the cylindrical section, perpendi-
cular to the generatrix: this is the “hoop” winding.
4
Roland Lucas
The entire part is then cured in an oven, with temperature (from 60° to
150°C) and duration (approximately 20 h) depending on the material used;
then the mandrel is removed. If it is an agglomerate of sand, a hydraulic
process is used to disintegrate the mandrel. The manufacturing process ends
with final machining. A series of tests is performed before delivery, i.e.,
ultrasound tests for structural integrity of the winding and the bonding of the
internal thermal insulation.
1.2. 1.2. Tactical missiles and rockets
Similar manufacturing processes are used for both tactical missiles and
rockets. A comparison between metal cases and cases made of fiber-
reinforced plastics is provided in ref. [4].
(a) Metal cases
The selection of manufacturing technique is based on the performance
requirements and includes:
• Helical wrapped-welded techniques, which are very well suited for large
industrial production.
• Wrapped-welded techniques along the length of the generatrix, used for
mid-size or small production runs;
• Flow forming, which does away with the drawbacks of welding along the
generatrix and has the advantage of very good precision and very good
inside surface conditions — this technique can be used for large-scale
production but requires substantial investments.
• Metallic strips which are first coated with an adhesive and then wound in
an helical configuration on a mandrel [5]. The number of layers wound is
a function of the thickness desired. This technique allows the manufacture
of metal cases with a very high level of mechanical strength under normal
operational conditions and, according to the inventors of the process,
shows specific advantages in the field of insensitive munitions. In the case
of unplanned stimuli (fire, bullet impact) resulting in the ignition of the
propellant inside the case, the strip laminate technique prevents the usual
explosion caused by confinement of the gases until rupture. Composite
material cases may offer similar advantages.
As a rule the manufacturing processes described above require that the end
closures, which are press-forged and machined, be welded to the case.
Sometimes the assembly of the forward end closure and the case, press-
forged, is accomplished by a flow forming process to minimize the number of
weld beads.
Because of the scale of industrial production, manufacturing costs require
the use of metal that can be welded and machined, and that is not too
Propulsion Elements for Solid Rocket Motors
5
expensive. Steel type AMS 6520 is commonly used for tactical engines. The
machining technology for this type of steel allows a minimum thickness of
approximately 1 mm.
Aluminum-copper (AMS 2014) and aluminum-zinc-magnesium (AMS
7075) alloys are also used for small-caliber rockets.
(b) Wound composite material cases
Specific performance characteristics of metals (modulus E and maximum
strength cr R divided by density p) are at best equal or inferior to the
characteristics of wound fiberglass. Composite materials such as glass-epoxy,
kevlar-epoxy and carbon-epoxy are used when performance requirements
are important. However, with these materials, strain/stress induced through
pressurization or TVC loads induced by ignition or TVC, may lead to
significant hoop strains (1-2%), causing greater problems for the structural
integrity of the propellant grain. Nevertheless, the winding technique is
increasingly used for the production of tactical missile cases [6,7], and
rockets [8]. The French company “Societe Europeenne de Propulsion” [9]
has developed an interesting process using a method called structural
assembly. The casting-curing cycle of the propellant grain is done in a rubber
tube. The whole, serving as a mandrel, is then wrapped with impregnated
filaments, thereby integrating the forward- and aft-end closures and, if
necessary, a blast tube.
1.2.2. Propellant grain
Two main configurations — free-standing grain and case-bonded grain
— with various central port geometries are used to fulfill the required
performance objectives.
• Free-standing grains. Free-standing grains are contained inside a cylin-
drical plastic cartridge (PVC, etc.). They are secured inside the case by
various support elements such as wedges, springs or grids.
• Case-bonded grains. These are obtained by casting the propellant, before
polymerization has occurred, directly into a case already provided with
thermal insulation. Additional manufacturing steps (molding, curing,
machining, control) required for the propellant grain are performed on
the loaded case.
1.2.3. Thermal insulation
The combustion temperature of propellant grains, ranging from approxi-
mately 1500 to 3500 K, requires the protection of the inside surface of the
case.
6
Roland Lucas
The design of the internal insulation involves the following four major
steps [10]:
• analysis of the internal thermal insulation environment: the nature of the
propellant gases, internal aerodynamics, etc.;
• selection of the material: reduced scale tests designed to assess specimens
in conditions simulating firing are performed;
• determination of the thickness in the various areas of the case necessary
to withstand the heat;
• determination of the dimensions and thickness needed to withstand
mechanical strains on the case and propellant grain.
In areas where flow erosion is high (high gas velocity in the vicinity of the
case wall), dense and possibly even rigid materials made of asbestos, silicate
and carbon fibers impregnated with a heat-proof resin (phenolic, polyamide)
may be used. Today, however, elastomers are being increasingly preferred to
these types of material. The use of elastomers has allowed significant
improvements in insulation by the addition of a reinforcing filler. Due to the
ban on asbestos filler, which has been used for many years, alternate
insulation materials have been developed as a replacement for the asbestos-
containing materials [11]. These reinforcing fillers are either in the form of
fibers (silicate, kevlar and carbon) or in the form of powder fillers (silicate and
carbon). Various densities can be obtained, in order to decrease the weight of
inert parts in the motor.
Thermal insulation for the cylindrical part of the case, which is exposed
only at the end of burning, can be provided by the liner, a rubber compound
with low fillers that is sprayed. The liner’s main function is to allow a good
bond between the propellant and the case or the thermal rubber compound.
Industrial production and the characteristics of this type of material are
specifically discussed in Chapter 13.
1.2.4 . The nozzle
The general shape of a nozzle (Fig. 2), called the nozzle profile, includes
three major parts:
• the convergent zone of the nozzle, which channels the flow of propellant
combustion gases;
• the throat: selection of throat dimensions determines the operating point
of the rocket motor;
• the exit cone of the nozzle, which increases the exhaust velocity of the
gases in their expansion phase, consequently improving the propulsive
effect.
Since 1970, thermal and physical property improvements of the materials
with, on the one hand, developments of new computer codes and, on the
Propulsion Elements for Solid Rocket Motors
7
other hand, performance of experimental studies, have made possible impor-
tant nozzle design improvements [12]. Currently, the shape and complexity
of a nozzle depend on the expected level of performance and on the field of
application of the rocket motor (space, ballistic missiles, tactical missiles). Its
design requires knowledge of the following parameters [13]:
• Internal operating pressure of the motor, which affects the structural
integrity of the nozzle and the ablation of the thermal materials.
• Burning time, often negligible for small rocket motors (a few seconds) but
in the case of large rocket motors (measured by the minute) an essential
factor in the determination of the thickness required to withstand thermal
transfer.
• Throat diameter, which will determine the operating pressure.
• Type of propellant used: the gases and the propellant’s burning tempera-
ture determine the selection of the thermal materials.
• Space available; often a function of equipment necessary for the guidance
of the missile; for example, the nozzles located at the end of a blast tube
on some tactical engines.
• Expansion ratio (exit cone area A s versus nozzle throat area A t , i.e.
£ = AJA t ) must allow a pressure in the exit section equal to the ambient
pressure to allow maximum efficiency. Because space is usually limited on
ballistic missiles, the concept of the extendible nozzle exit cone (during
flight) permits an increase in this ratio during operation.
• Submergence of the nozzle into the burning chamber, defined as the ratio
of the integrated length versus total length, to minimize the external part
of the nozzle. This technology is used particularly on ballistic and space
8
Roland Lucas
missiles. The external nozzle, less complex technologically and less costly,
is used for the propulsion of tactical missiles and in situations where
overall vehicle length is not a constraint. The nozzle is sometimes placed
at the end of an insulated metal tube. Use of this blast tube provides space
for the devices that activate the steering controls of the missile.
• Thrust vector control which, in ballistics and space motors, uses the
principle of a movable nozzle permitting thrust vector control angles
ranging from 3° to 15°. The various mechanical systems used include
flexible bearing, ball and socket, hydraulic bearing and rotatable exit
cone. These techniques cannot be used with tactical missiles. They are
replaced by aerodynamic systems — fins — acting on the nozzle jet or,
when the atmosphere is sufficiently dense, aerodynamic fins mounted on
the case. Non-guided rockets require a spinning action to ensure flight
stability. This requirement is taken into account when designing the
nozzle. Various systems such as gas deflectors and slanted slots are
included, which use the gas flow in the exit cone, or special motors are
included to start the spin.
• Interface with the case, which must take into account the geometry
selected — nozzle integration or maximum displacement of the nozzle
— and the concern to minimize inert part mass.
• Performance, cost, reliability, environment and service life; often conflict-
ing parameters which are used to select the final technical design.
In the case of ballistic and space missiles, performance requirements often
lead to the design of materials with good thermal and mechanical stress
characteristics, which are well suited for use in the production of large parts.
There are currently three major families:
• Traditional composite materials (carbon-epoxy, glass-epoxy) for the
body of the nozzle, sometimes replaced by metals (steel, aluminum).
• Ablative materials, made of refractory fiber reinforcements such as
carbon, graphite and silica and a matrix obtained from the polymeriza-
tion of a resin, generally phenolic. These materials are generally used for
the duct and as insulation between the duct and the nozzle body.
• Thermostable insulators with a refractory matrix and ceramic or rein-
forcement carbon. They provide both insulation and structural integrity.
They have no degassing at high temperatures and are used mainly for the
nozzle walls. Carbon-carbon is particularly well suited for the manufac-
ture of parts from a single block. It is composed of a carbon reinforcement
(fabrics, fibers, pultruded sticks) and a carbon matrix obtained by a
multistep liquid or gas process (densification process). It is known for its
low density (1.5-2) and related excellent structural integrity at high
temperatures. The design and development of new solid rocket motor
(SRM) nozzles may incorporate these materials in several ways [15].
Propulsion Elements for Solid Rocket Motors
9
Frequently the entrance and throat region will be fabricated as a single
piece of carbon-carbon material called an ITE (integral throat-entrance).
A variation of this application is a single-piece throat, exit cone compo-
nent called an ITEC or integral throat-exit-cone [16]. Carbon-carbon
materials are used to construct very thin-walled structures for fixed and
extendable segments of exit cones.
Finally a new concept is under development: the nozzleless solid rocket
motor. This approach may use a high-strength, low-burn-rate propellant to
form a nozzle. In this case [14], SRM cost reductions of 10-20% are expected.
1.2.5 . The ignition system
The ignition system brings the energy necessary to the surface of the
propellant to start burning. There are three stages:
• Initiator: a pyrotechnic element designed to transform an ignition signal
such as shock, electrical impulse or light into the steady burning of a
pyrotechnic substance.
• Booster charge : a charge, powder, pellets or propellant micro-rocket that
transmits the flame between the primer and the main grain.
• Main charge: a charge, powder, pellets or propellant rocket that ignites
the propellant grain.
Ignition systems for large propellant grains (ballistic missiles, space) use this
three-stage process. The main charge burns for a few tenths of a second,
delivering a discharge approximately a tenth of the flow rate of the propellant
grain.
Ignition systems for small propellant grains are usually limited to a primer
linked to a primary powder charge (instantaneous and very high release of
gases during a few milliseconds) or a primer and an increment (a few tens of
milliseconds).
The ignition materials have a high specific energy. They are designed to
release either gases or solid particles, based on applications. Pyrotechnic
ignition compounds include one or several generally metallic reducers, e.g.,
Al, Mg, B, Zn, C, and others, and one or several oxidizers or metallic oxides,
e.g., NH4CIO4, CuO, Fe 2 0 3 , BaO, Ba0 2 , and others. Binary ignition
compounds are the most used. Sometimes such compounds are designed to
fit very specific applications, as was the case of the IFOC system (Initiateur a
Fonctionnement par Onde de Choc; in English: shock wave primer), used on
the Ariane rocket [17]. This compound is ignited by a shock wave and must
not under any circumstances detonate.
10 Roland Lucas
2. Fundamental Equations of Internal Ballistics
2.1. INTRODUCTION
The objective of internal ballistics of propellant rocket motor is to provide
the motor design engineer with the means to predict or understand the
burning characteristics.
The following paragraphs provide a closer view of rocket motor operation.
For more detailed information on the equations below, the reader is referred
to classic books or technical papers [18-20].
To begin with, there are two fundamental definitions [21]:
• Burning pressure : this is the static pressure measured at the head end of
the internal gas flow; in other words, it is the pressure at the forward end
of the combustion chamber. It is, by definition, an absolute pressure.
• Burning rate : this is the linear regression rate of the flame edge, measured
at a specific time and a specific distance on the propellant burning
surface. The steady-state burning rate of a propellant (excluding the
ignition phase and thrust tail-off) is defined by the ratio of minimum web
to be burned (minimum distance traveled by the flame edge from the start
of combustion to the time the flame reaches the outside contour of the
grain) versus steady-state burning time. The burning rate is a function of
the combustion chamber pressure.
2.2. PROPELLANT GRAIN FLOW RATE
For preliminary calculations it may be assumed that propellants burn in
parallel layers, and that the burning rate is only a function of the pressure.
Under these conditions the flow rate resulting from the combustion at a given
time is:
q = p-S-v (1)
where p is the density of the propellant, S the burning surface and v the
burning rate of the propellant at a given time.
2.3. NOZZLE FLOW RATE AND DISCHARGE COEFFICIENT
A nozzle, like any other opening, allows a flow rate which is proportional
to the opening area — here, the area of the throat, A t — and to the pressure
upstream of the nozzle — here, chamber pressure, p.
The proportionality coefficient is called the propellant discharge coeffi-
cient, indicated by C D .
11
Propulsion Elements for Solid Rocket Motors
Where q' is the gas flow rate passing through the nozzle,
q' = C D -p-A t (2)
where p is combustion pressure at a given time.
Presuming that gases are ideal, it can be shown [19,20] that coefficient C D
is affected only by the nature and temperature of the gases flowing through
the nozzle, or
C D —
r (y) = y
y + l
y + l/2(y — 1 )
( 3 )
where:
T is the combustion temperature (ranging from 2000 to 3000 K);
y is the ratio of specific heats of combustion gases at constant pressure and
constant volume (y = c p /c v with an approximate value of 1.2);
r is RjJt where R is the universal gas constant (8.134 J/kg-K) and M is
the molar weight in kg (approximately 29 x 10 _3 kg for propellant
gases).
Remark: T and y are not very susceptible to pressure variations, particularly
in the case of propellant with a low level of aluminum. Therefore, in many
cases, the independence of C D from pressure is accepted.
The discharge coefficient is expressed in seconds/meter, i.e. the inverse of
the flow rate: meters/second. A typical value of C D is in the range of
6.5 x 10 -4 s/m. The average experimental flow rate coefficient is calculated
by using eqn (4), which is obtained from eqn (2) by calculating the integral of
both sides of the equation as a function of the burning time of the propellant
grain:
r — (4)
where M p is the mass of propellant ejected and p(t\ A t (t\ the equations for
evolution of chamber pressure and of the nozzle throat area during combus-
tion.
2.4. ROCKET MOTOR OPERATING POINT; KLEMMUNG
(BURNING AREA TO THROAT AREA RATIO)
2.4.1. Operating point
The rocket motor operation point corresponds to the equality of the gas
flow rates:
• created from the combustion of the propellant grain;
• ejected by the nozzle.
12
Roland Lucas
Based on eqns (1) and (2), this relation is given by:
p-S-v = C D p-A t (5)
Remark: For preliminary calculations this equation does not take into
account the volume of gas filling the space resulting from the combustion of
the propellant inside the combustion chamber.
Relation (5) can also be written:
C D A t
v = --*-P
P s
(6)
According to the above equations, at any given time in the combustion
chamber of a rocket motor (A t and S having values specific to the rocket
motor) containing a known propellant (which defines C D and p\ the burning
rate is proportional to pressure p.
The burning rate of a propellant, in terms of an intrinsic property of the
material, is easily obtained by using small motors which have a constant
propellant burning area S, and so a constant operation pressure p. (Refer to
Chapter 4, Section 4). Within a common range of pressure (from 3 to 30 MPa
depending on the propellant), several successive values may be obtained by
selecting different values of the AJS ratio.
A law defined by the following equation:
v = ap n (n < 1) (7)
is often found to be a good expression of the phenomena.
The rocket motor operating point (v Q9 p 0 ) at a given time will be such that
eqns (6) and (7) are simultaneously validated.
On a graph with coordinates v and p (Fig. 3), the rocket motor operating
Fig. 1.3. Operating point of a rocket motor.
Propulsion Elements for Solid Rocket Motors 13
point is located at the intersection of the straight line of eqn (6) and the curve
of eqn (7).
2.4.2 . Klemmung
The klemmung of a rocket motor is the ratio between the propellant
burning surface area and the throat nozzle area.
Equation (6) can be written in the form:
C D 1
v = p
P K P
( 8 )
( 9 )
Figure 3 shows that for a given propellant grain (law v = ap n determined),
the operating point of a rocket motor ( v Q , p Q ) is a function of the value of the
klemmung.
Specifically, all other parameters being equal, a fluctuation in the value of
K , either voluntarily induced to obey a thrust law or involuntary and
deriving from an operational defect (e.g. a crack in the propellant grain
causing a sudden increase of S, or a nozzle obstruction), results in a shift
toward a new operating point corresponding to a new burning pressure ( p ' Q )
and a new burning rate ( v ' Q ).
2.5. USEFUL EQUATIONS
Equation (5) can be used in the form:
effect of the burning law:
p-Sv
C D • A t
v = a- p n (n < 1)
Equation (10) can be used in the form:
P
n- 1
p-S-a
C D • A t
( 10 )
(H)
This last equation is useful for preliminary propellant grain design, excluding
combustion phenomena covered in greater detail in Chapter 4.
With any given grain using a known propellant, there is:
14
Roland Lucas
p : constant;
a and n: presumed constant in the pressure zone analyzed;
C D : presumed constant for the major part of the pressure rise of the
combustion;
A { : generally fluctuates so little that it can be assumed constant.
Relation (11) shows that, once the equation of the evolution of grain
burning surface is known, the equation for propellant internal pressure can
be determined, thereby demonstrating the importance of determining the
initial burning surface, then calculating its evolution to be able to find the
internal pressure law of the rocket motor best suited for the mission of the
missile.
2.6. TEMPERATURE COEFFICIENTS
Propellant temperature affects the rate of burning. Because of the wide
temperature ranges required for some tactical all-weather missiles, from
— 45°C to 60°C or more, a detailed knowledge of these variations is
mandatory.
The equations for burning rate and pressure at various temperatures can
be calculated from measurements. Curves i; max and v min in Fig. 3 are an
example of data obtained.
When characterizing the temperature sensitivity of a propellant, a constant
klemmung ratio is generally preferred because it corresponds to a motor
operating at various temperatures.
Coefficient n K expressing the temperature sensitivity is written in the form:
—
Approximately 0.25% for 1°C is a typical value found in composite
propellants.
When u max and v min correspond to extreme temperature requirements for a
tactical missile, Fig. 3 shows that the value of operating pressure can vary
between p max and p min simply due to temperature changes.
Temperature sensitivity at constant pressure, 7i p , is sometimes required. It
is given by:
n
p
1
v
with a burning rate law v = ap n , it is easily demonstrated that:
n p = (1 - n)-n K
Propulsion Elements for Solid Rocket Motors
15
3. Rocket Motor Thrust
3.1. THEORY OF OPERATION OF A NOZZLE
The nozzle expansion process involves the study of very complex transfor-
mations, chemical reactions, heat transfer, gas flow, etc.
Modelling the nozzle operation necessitates the use of simplifying assump-
tions that will lead to a model with results close to the actual performance of
the rocket motor it represents.
Some aspects of this question have been covered in the specialized
literature [18-20].
Some of the most important simplifying assumptions are:
• combustion and subsequent expansion of the combustion products are
two separate phenomena that happen respectively in the combustion
chamber and in the nozzle;
• the expansion in the nozzle is an isentropic phenomenon, in other words,
adiabatic and reversible;
• one-dimensional flow;
• gas flow velocity at the entrance of the nozzle is very low and the gas
kinetic energy is negligible;
• gas flow through the nozzle occurs without separating from the wall.
Combustion gases are known to remain in the nozzle for a period of 10" 4 to
10" 3 s; that information permits us to set the solution between two extreme
models:
• the time needed to reach chemical balance is long compared with the time
the gases remain in the nozzle; the gas composition does not evolve: it is a
frozen equilibrium flow;
• the time needed to reach chemical balance is short compared with the
time the gases remain in the nozzle; the gas remains in chemical
equilibrium as a function of the local temperature and pressure through
the expansion and in each area of the nozzle: it is a shifting equilibrium
flow.
Working with the assumptions given above, a simplified method can be used
by presuming that the combustion products are ideal with a constant
molecular weight and y.
Using the following variables:
p, T and p : pressure, temperature and density of the gases;
V: gas flow velocity;
A: a cross-section of the nozzle;
R \
r = -z ;
R:
universal gas constant
16
Roland Lucas
a : the speed of sound (a = ^JyrT)\
M: the Mach number (M = V/a);
and the following equations:
p „ RT
the Manotte law: - = rT = — —
continuity equation: p ■ A • v = csf e
Saint-Venant equation: F 2 = 2*c p * AT
Mayer formula: c p — c v = r = —
and using the following subscripts:
• index 0: for the values of the parameters at the beginning of the
convergent zone of the nozzle, in other words the values obtained during
the propellant combustion;
• index t: for the values of the parameters at the throat of the nozzle;
• index s: for the values of the parameters at the exit plane of the nozzle;
The following is demonstrated:
3. 1. 1. The Hugoniot formula
dA
~A
dV
(M 2 - 1)
showing that, on a convergent-divergent nozzle:
• gas velocity increases continuously;
• gas velocity is equal to the speed of sound at the throat section (M = 1).
3. 1.2. The existence of a maximum exhaust
velocity
This velocity is reached through isentropic expansion of the gases, until
absolute vacuum.
3. 1.3. The existence of various relationships
between the operational parameters
• In any section of the nozzle:
l.
Po VV \Po J
Propulsion Elements for Solid Rocket Motors
17
• At the nozzle throat:
T x _ 2
T 0 ~i+~ I
• At the exit cone section:
Vs =
where p Q /p s is the expansion ratio.
Because exhaust velocity is of primary importance in the determination of
thrust, we need to write in its complete form:
Vs =
( 12 )
where V s increases when T c does or when the molar mass M of the exhaust
gases decreases.
3.2. DETERMINATION OF THE THRUST
Where p a is the ambient pressure and q the gas mass flow rate of the nozzle:
f = q-K + (Ps - pMs
This equation demonstrates:
• that thrust increases when ambient pressure (p a ) decreases. Thrust is
maximum in vacuum, i.e.:
F vacuum = q • V s T p s • A s
• and that for a given ambient pressure (constant p a ) after taking into
account the differential equation:
dF = V s dq + q-dV s + A s - d(p s - p a ) + (p s - p a ) • d A s
where q and p a are constant, thrust is maximum when p s = p a , that is:
F = q-K
in which case we have the optimum expansion ratio of the nozzle; p s is a
function of p Q and of the geometry of the nozzle and, because of that, it cannot
be constantly equal to p a , which varies during flight.
• When p s > p a the jet bursts at the exit cone. It is under-expanded.
• When p s < p a the jet separates from the wall of the nozzle. It is
over-expanded. (The Summerfield criterion, which is valid for the half-
18
Roland Lucas
angles of the exit cone of a nozzle smaller than 15°, indicates that
separation occurs in an area where pressure is close to 0.4 p a .)
3.3. THRUST COEFFICIENT
For practical reasons related to the design of the propellant grain, it is
useful to use a proportionality coefficient, which is the ratio between the
thrust on the one hand and the chamber pressure and throat area on the
other hand. The relation is:
F = C F -p 0 A t (13)
Combining with eqns (12) and (13), it is solved by:
C F is a parameter that does not depend on units of measure and depends
solely on combustion gases (y) of the ratio between sections e — A s /A t and on
the ratio p 0 /p a -(p 0 /Ps is expressed only as a function of y and of AJA t ).
C F indicates the efficiency of a nozzle for a given propellant grain and given
nozzle geometry. Figure 4 shows the evolution of C F as a function of the ratio
e = AJA t for various values for the p Q /p a ratio.
These same results can be displayed in the form of tables, based on the
values on y.
Fig. 1.4. C F diagram.
19
Propulsion Elements for Solid Rocket Motors
4. Specific Impulse
4.1. INTRODUCTION
Suppose we have several rocket motors with identical structures (shape
and equipment) and nozzles, and loaded with different propellant grains.
A comparison of their performance is easily done by measuring the
intensity of the thrust F obtained by each of the motors during operation.
All things being equal, the various compositions of propellant grains can
be compared by dividing thrust F obtained by the weight flow rate of
propellant burned.
This ratio — the thrust obtained versus the weight flow rate — for a given
rocket motor allows us to determine the intrinsic characteristics of the
propellant grain used.
This is known as the specific impulse of the propellant grain. Because its
dimensional equation is time, this value is expressed in seconds. At this point
it is already clear that, because specific impulse can only be measured through
the operation of a rocket motor, its experimental measurement is highly
dependent on the rocket motor and its operating point.
4.2. DEFINITIONS AND RELATIONS
Instantaneous specific impulse is the ratio of thrust versus the weight flow
rate of the propellant at a particular instant; it is given by:
L =
0o*0
(14)
where g 0 is the standard acceleration due to gravity ( g 0 = 9.80665 m/s 2 ) and
q the mass flow rate of the propellant.
From the previous equation we can write:
F = pC ¥ A x j C F
QoG QoPCd A i S 0oQ>
(15)
To measure performance of the propellant it is preferable, for practical
reasons, to take into account total duration of combustion. By combining the
second side of eqn (14) with the total combustion time (t c ), we obtain the
average specific impulse of the propellant or of the rocket motor:
/
sm
9 o’Afp
where M p is the total mass of propellant burned.
20
Roland Lucas
The integral of thrust F as a function of total combustion time (t c ) is called
the total impulse of the rocket motor; it is given by:
Based on the preceding equations, we can deduce that:
and
(16)
^Ft 9 o * M p * / Sm
(17)
4.3. PRACTICAL APPLICATIONS
The definitions introduced in the preceding paragraph and related equa-
tions are used by the designers to guide them in the selection of the best
performances.
4.3. 1. Propellant formulation
Equation (15) shows a direct connection between specific impulse and
nozzle discharge coefficient C D . Based on the expression for C D (see Section
2.3 of this chapter), we obtain a proportionality relationship between / s and
yjrjjl . To design highly energetic propellants the researcher will seek the
propellants with high combustion temperatures T that produce combustion
gases with the lowest possible molar mass.
4.3.2. Preliminary propellant grain design
Preliminary design analyses of a rocket motor always require the determi-
nation of a thrust level F which must be available for a length of time t
necessary to perform the assigned mission.
This requirement is translated into the level of total impulse to be
obtained:
/ ft — Ext.
Using eqn (17) and based on the value selected for the average specific
impulse (/ sm ), the expert is able to deduce the required weight of the
corresponding propellant. This equation is of great use for all calculations for
preliminary propellant grain design.
21
Propulsion Elements for Solid Rocket Motors
4 . 3 . 5 . Preliminary missile design
A rocket with a total mass M moves vertically at a speed K Where K is the
resultant from aerodynamic forces expressing air drag and F the thrust
delivered by the rocket motor, the equation of motion is:
dV
M — = F + M -g + R
d t
dV
= q-00-fs + Mg + R
dV
d t
1 d M
M’~dT
' 9 °' Is+9 + iti
By integrating this equation between r 0 and t x which correspond to
ignition and propellant burn-out (t c ~ t x — t 0 ) and neglecting air drag the
velocity increase is:
= g 0 -/ s -ln^ +
Assuming that I s and g remain constant during the t c combustion time and
where:
M 0 = total weight of the rocket (M 0 = M p +
M p = propellant weight
M i = rocket weight at burn-out
and
p = the density of the propellant
v = the volume of the propellant grain
we can write the following equation:
AK = 0 O ./ S .ln 1 +
pv
M x
+ 9 ’ t c
All other things being equal (g, t c ), the velocity increase of the rocket is
therefore a function of:
do ■ I* ■ In
This equation is very useful for preliminary design analyses.
• When M p = pv is small compared to (the first stages of ballistic
missiles), AV becomes a function of:
do'h-
Pj_v
Mi
( 22 )
22
Roland Lucas
and the product p • v J 5 is an important criterion for the comparison of
propellant grains.
• When M p = p-v is high compared to M 1 (the last stages of ballistic
missiles), AV is a function of:
p • v
JT,
in which case p intervenes only through its logarithm. Specific impulse
alone is then an interesting criterion for the comparison of propellants.
These results suggest that propellants could be compared using a perfor-
mance index such as:
J s • p* where 0 < a < 1
where a is dependent on the rocket motor in which the propellant is to be
used. This theory has been developed in various references [18,22].
4.4. DETERMINATION OF THE AVERAGE STANDARD SPECIFIC
IMPULSE
Experimental measurement of specific impulse is available only through
operating a rocket motor. Consequently, its value is related to the rocket
motor.
In addition, eqn (15):
/
s r'
9o ' C D
shows that for a given propellant (y constant), the value of / s is dependent on
C F , therefore on the ratio of sections s = AJA t and p 0 /p a which are inherent
to the operating characteristics in the rocket motor.
These remarks illustrate why there is a certain amount of confusion
concerning the comparison of the performance of propellants. To be fully
convinced, it should be enough to note:
• that p Q is the internal operating pressure of the rocket motor and is
therefore related to the combustion chamber characteristics;
• that p a is the pressure outside of the missile and is therefore related to
ambient test conditions;
• that e is related to the geometry characteristics of the nozzle and their
evolution during operation.
Luckily, it is commonly agreed that specific impulse is the parameter that
should be used to discuss the performance of propellant grains or rocket
motors. This means that, in practice, the exact operating conditions of a
rocket motor must be established to allow measurement of the average
standard specific impulse:
Propulsion Elements for Solid Rocket Motors
23
• The expansion ratio p 0 to p s has been established. Its value, in the United
States, has been set at 68, where p 0 is 1000 psi and p s = p a is 14.7 psi
(atmospheric pressure under normal conditions). In France, p D was in the
past assigned 70 atmospheres and a value of p s = p a of 1 atmosphere; this
ratio is therefore 70.
• The nozzle must be adjusted for the ambient pressure at sea level:
p s = p a = 0.10133 MPa.
• The exit area is shaped like a cone with a 15° half-angle.
To obtain comparable data between propellants, the tests must be per-
formed with identical rocket motors, known as standard rocket motors. The
propellant grain geometries used are well suited to obtain the desired precise
data (e.g. a combustion pressure that is as constant as possible, geometric
parameters that are simple to measure, etc.).
Two types of geometry are commonly used; they are described in greater
detail in Chapter 3, Section 5.5. They are:
• the 10-branch star-shaped propellant grains, named ‘Mimosa 5 ;
• the cylindrical shape, a propellant grain from the United States, named
‘Bates’.
These rocket motors are manufactured and tested very carefully to ensure
good reproducibility and high-quality results. There may, however, still be
some small differences from the standard operating conditions defined above.
After analyzing the results, the necessary compensations are calculated; a
detailed discussion of these corrective measures is found in Chapter 3, Section
5.9; they are based on the proportionality laws between specific impulse and
thrust coefficient (C F ). The results of these measurements and calculations
allow us to obtain the average standard specific impulse of the propellant,
expressed by I s sm .
In conclusion, we see that great caution is necessary when discussing
specific impulse. Indeed, a rigorous performance comparison between vari-
ous propellants requires:
• identical rocket motors (shape, mass, insulation, shape and material of
the nozzle, etc.);
• operating points corresponding to standard conditions;
• identical unit systems;
• test conditions and equipment sufficient to secure a good level of
precision.
4.5. AVERAGE SPECIFIC IMPULSE OF A ROCKET MOTOR
For a given propellant it is possible to assess the performance of the future
rocket motor by determining a predicted average specific impulse.
There are various methods to calculate and optimize the performance of a
24
Roland Lucas
rocket motor. An excellent synthesis of the research done by Working Group
17 under the AGARD (Advisory Group for Aerospace Research and
Development) is available [23], in which the three main steps of this process
are well described:
4.5 . 1. Calculation of the theoretical specific
impulse of the propellant
This step uses the thermodynamics computer programs based on main
algorithms developed by the Lewis Research Center of NASA [24]. In
addition, there are two complementary data banks on thermodynamic
properties of the various components of the propellants and other products
likely to result from combustion and subroutines tailored to the needs of the
user (presentation of results). The use of this software and various thermo-
dynamic calculations performed are discussed in depth in Chapter 3.
Based on the chemical composition of the propellant, this software
program calculates the various thermochemical characteristics of the com-
bustion gases and the theoretical specific impulse of an ideal rocket motor
having no losses, for the required operating point ( p Q , p a and e). The major
simplifying assumptions are:
• uniaxial, isentropic and non- viscous flow;
• chemical equilibrium of the gases during expansion;
• kinetic and thermal equilibrium between the solid and gaseous phases of
the flow.
4.5.2. Determination of losses due to flow
conditions in the nozzle
These losses result from the discrepancies between real properties of the
flow of the gaseous mixture and the characteristics corresponding to the
simplifying assumptions above. They belong, in general, to the following six
categories:
• Losses through flow expansion because the flow is in fact bidimensional.
They are a function of the half-angle of the exit cone and of its convex
shape.
• Two-phase losses, resulting from velocity and temperature lag between
the solid and the gaseous phases.
• Boundary layer losses, caused by the viscosity effect and by the heat
exchange at the nozzle wall.
• Losses through chemical kinetics because of a delay in the establishment
of chemical equilibrium of the gas flow.
• Losses due to the submergence of the nozzle into the propellant grain,
resulting in a modification of the flow at the inlet of the nozzle.
Propulsion Elements for Solid Rocket Motors 25
• Losses due to erosion of the throat area through ablation, resulting in a
decrease of nozzle expansion ratio.
4.5.3. Determination of losses due to chamber
combustion conditions
With a radial burning propellant grain these losses are fairly limited
compared to the losses due to the flow conditions in the nozzle. They are
mainly caused by heat exchange at the walls and incomplete combustion.
The research done by Working Group 17 AGARD [23] permits compar-
ison of the performance predictions done by various companies, using the
steps described above. These forecasts were done for two different rocket
motors. They were later compared to the experimental results.
Average specific impulse
Rocket motor
forecast
Actual measurements
no. 1
289.6-294.5 s according to various companies
293.12 s
no. 2
292.8-299.1 s according to various companies
296.7 s
Complex programs are necessary to estimate the average specific impulse
of a rocket motor. With such tools the designer is also able to improve the
profile of the nozzle duct and, as a result, to optimize the performance of the
rocket motor. The process involves successive iterations between profile
modifications and calculation of corresponding losses, while at the same time
taking into account the thermal characteristics of the materials.
4.6. EFFICIENCY
4.6. 1. Propulsive efficiency
An estimation of the losses in the nozzle will be made experimentally by
calculating the propulsive efficiency of the nozzle:
with:
C F obtained from the theoretical calculations described in the preceding
section;
C F obtained by using the firing data in the equation:
sT- . fF-dt
dt
where A t is the average throat area during firing.
26 Roland Lucas
4.6.2 . Combustion efficiency
Similarly, the combustion efficiency, which will indicate losses inside the
combustion chamber, will be calculated by writing:
with:
C D obtained from the above theoretical calculation;
obtained by using the firing data in the equation:
r~ _ m p
D A t j p‘dt
where M p is the mass of propellant burned.
As a rule, losses inside the combustion chamber are limited and correspond
to about 10% of the losses in the nozzle. This rule does not apply, however, to
the end-burning propellant grains. In this particular case the importance of
thermal losses in the combustion chamber increases with the regression of the
flame front, leading to a drop of the specific impulse of the motor [25].
4. 6.3. Overall efficiency of the rocket motor
The overall efficiency accounts for all losses in the rocket motor (nozzle
and combustion chamber). It is written as a function of the average specific
impulse:
/ sm (measured)
rj = ;
/ sm (theoretical, without calculating the losses)
Based on the equations described in this section, we see that:
rj = q* -rj F
5. A Special Case: Ramjets and Ramrockets
5.1. GENERALITIES: AIR-BREATHING MOTORS
By definition, an air-breathing motor uses the oxygen in the air to function.
Consequently, unlike rocket propulsion, a rocket engine using an air-
breathing motor needs the outside environment to ensure its propulsion.
This type of motor is finding its application in the ramjet working
technology which, in spite of a rather early design — proposed in 1911 by
R. Lorin — is currently the object of renewed interest in the area of missile
Propulsion Elements for Solid Rocket Motors
27
propulsion [26,27]. However, their operation assumes the use of boosters to
allow reaching supersonic speeds.
During the propulsive phase of the ramjet the specific impulse (which is the
impulse supplied by the mass unit of burned propellant), because of its use of
atmospheric gases, is four to six times greater than the specific impulse of
conventional propellants. These values are significant, however, only under
operating conditions equivalent to those found during flight. For example,
under specific experimental conditions (Mach 2, altitude 0) and a chamber
pressure of 0.57 MPa, the average specific impulse will be in the range
1000-1300 s, depending on the propellant families.
5.2. DESCRIPTION OF A RAMJET
A typical ramjet includes the following components (see simplified drawing
in Fig. 5):
• An air inlet, followed by a divergent diffuser section, located between
sections 1 and 2, allowing the intake and compression (with temperature
rise) of the quantity of air required for combustion.
• A fuel injection and air/fuel mixing system, located between sections 2
and 2'. For solid propellant motors, called ducted rockets or ramrockets,
the liquid fuel is replaced by gases produced by the combustion of a
propellant grain located in a primary chamber. The injection of these
gases and their mixing with air takes place in an area located before the
combustion chamber (Fig. 6).
• A combustion chamber where the mixture is burned, also called the
secondary chamber (sections 2' to 3), where the temperature rises (to
approximately 2.200 K at 0.8 MPa in this particular case) at the same
time as the gas flow increases.
• An ejection system for the combustion products through a convergent-
divergent nozzle, assumed to be sonic at the throat (sections 3 to 5).
Fuel
Fig. 1.5. Drawing of a ramjet.
28
Roland Lucas
Fig. 1.6. Drawing of a solid-fuel ramjet.
To operate correctly, the ramjet must be ignited at supersonic speeds (around
Mach 1.5). It has been clearly established that this method of propulsion is of
no interest under Mach 1 beause the compression ratio is too low under such
conditions.
5.3. PRINCIPLES OF OPERATION
Let us assume that the ramjet is a hollow axisymmetric shape, placed in a
uniform supersonic flow with a velocity V 0 and equipped with an adjustable
cover to allow variations in the exit plane A 4 (Figs 5 and 7).
Three types of operational modes are possible:
5.3. 1. Subcritical mode
The cover is pulled back a little. The frontal shock wave is located in front
of the inlet. A thin-stream jet of cross-section A 0 in front of the shock
penetrates into the diffuser. When traversing the shock wave the flow
becomes subsonic and is subjected to a recompression inside the diffuser. In
the vicinity of the exit the flow accelerates and becomes sonic at S.
The resultant of the pressure force (internal pressure greater than external
pressure) is directed toward the front, creating a thrust. The subcritical rate is
characterized by a mass flow rate:
4m = Po ’ K) ’ (23)
5. 3. 2. Critical mode
The opening section S is further opened. The flow increases and the frontal
shock wave moves closer to the inlet. The mass flow rate reaches its
maximum value when the shock attaches itself to the rim of the air inlet:
4 m = Po-Vo-A 1
(24)
Propulsion Elements for Solid Rocket Motors
29
L
r
L
A 0 \A1
P>Po
Subcritical mode
v.
Aq Ai
P>
S
J
Po C
Critical mode
l
A<
L
P<P<L-r
0 > L
"fH!:
Aq A, n
Po
Supercritical mode
Fig. 1.7. Ramjet operating principles.
The flow in the diffuser is completely subsonic, the internal pressure
remains greater than the external pressure. A thrust forward results. This
operational rate corresponds to optimal performance.
5.3.3. Supercritical mode
When further increasing exit plane S, the external flow is not subject to any
modification (constant rate q m )\ the plane portion of the shock wave,
however, moves into the diffuser. The thrust/drag balance is either positive or
negative based on the position of the shock wave, because the internal
pressure in front of and behind the shock is respectively smaller and greater
than the atmospheric pressure.
5.4. EQUIVALENCE OF THERMAL AND MECHANICAL
OBSTRUCTIONS
Removing the rear obstruction, and assuming that we supply a certain
quantity Q of heat to the flow, between N and S: analyzing two neighboring
sections of the flow between which d Q is supplied, a demonstration based on
the classic laws of flow [28] leads to the equation:
(1 - M 2 )
dV
~v
d Q K 2 dA
T • p a 2 A
(25)
30
Roland Lucas
where:
K 2
dp
ds
(where s is the entropy of the flow gases);
a 2 = the square of the speed of sound;
V, p,p,T = velocity, density, pressure and temperature of the flow gases;
A = area of entrance section and M is the Mach number.
This equation shows that the addition of heat (d Q > 0) affects the velocity in
the same way as a reduction of the cross-section (dA < 0), which explains the
expression “thermal obstruction of the flow”.
5.5. PROPULSION EQUATIONS
Looking at the ramjet in Fig. 5: conventional thrust is determined by
applying the law of momentum [28,29].
F = p 5 A 5 (l + y M\) - p^je (1 + y Ml) - p 0 (A 5 - A 0 ) (26)
N.B. : The evolution of the value of a parameter is indicated with the value of
its index, which stands for the section analyzed. The index i is used for
generative pressure.
Assuming an operation at critical mode (e = A 0 /A x = 1) we use:
(1) Efficiency of the air intake
Pi2
r\oi = —
P iO
(2) The characteristics of the motor rating
Pi5
* 1 25 =
P\2
(3) The parameters of the geometry of the ejector
c 2 5 = 4^ and — = co(M 5 )
A 2 P i5
where to(M) = 1 +
i \ - y/y - 1
-M 2
(for an isentropic expansion of a thermally ideal gas, y is constant in
permanent rating).
(4) The evolution of cross-section A of a stream tube
A
X
1
M \y - 1-1 y +
2 + »
1 M 2 ]
V + 1 )
y + l/2(y — 1)
= I(M)
Propulsion Elements for Solid Rocket Motors 31
where A c (the critical area) indicates the surface that would be taken by
this flow tube if the isentropic expansion reached M = 1.
(5) The equations
which, by writing the conservation of flow from infinitely upstream to
section A 2 (p io A co = p i2 A c2 \ leads to:
„ _ Pi2 _ A i Z2
n ° 2 ~P, 0~A 2 'Zo
with the assumption (e = AJA i = 1) which has been selected.
(6) External drag
^ext Po i A 5 ^ 0 )
Equation (26) can be written:
F
Po A 2
(JO*
<^2S - »72S *=- (1 + y Ml)
(1 +yM 0 2 )
]-
^ ext
Po A 2
(27)
or:
Po A :
= rj 02 ^
Po A 2
(28)
S' depends solely on the geometry of the ejector (a 25 , M 5 ) on the flight
Mach number and on the motor rating ( rj 25 , M 2 ). Any increase A^ o2 of
efficiency in the air intake results, all other things being equal, in a
proportional increase of the net thrust:
= S' * A^q2
Finally, it is normal to use the value of thrust related to section A 5 . A
thrust coefficient is determined:
C F —
F
1/2*7* Mq • p 0 -~A~ 5
In the case of critical operation, eqn (26) is used to write:
Ps 1 +
Po yMl
( 29 )
32 Roland Lucas
Bibliography
1. Bruner, G., La qualite metallurgique dans les industries aerospatiales, V Aeronaut ique el
rAstronautique, 83, April 1980, pp. 13-18.
2. Parr, C. H., Composite for propulsion applications — an overview, 24th Joint Propulsion
Conference, Boston, Massachusetts, AIAA-88-3127, July 1988.
3. Denost, J. P., Conception des structures de propul seurs bobinees, Design Methods in Solid
Rocket Motors , AGARD-LS-150, 1987, pp. 23-44.
4. Lang rock, W. J., Solid rocket motor case design, Design Methods in Solid Rocket Motors ,
AGARD-LS-150, revised version 1988, pp. 1-16.
5. Badham, H. and Throp, G. P., Considerations for designers of cases for small solid
propellant rocket motors, Design Methods in Solid Rocket Motors, AGARD-LS-150, 1987,
pp. 1-20.
6. Evans, P. R., Composite motor case design, Design Methods in Solid Rocket Motors,
AGARD-LS-150, 1987, pp. 4.1-4.11.
7. Gerlach, H., Composite motor cases for tactical rockets, 24th Joint Propulsion Conference,
Boston, Massachusetts, AIAA-88-3327, July 1988.
8. Magness, R. W., Development of a high performance rocket motor for the VT-1 tactical
missile, 24th Joint Propulsion Conference, Boston, Massachusetts, AIAA-88-3325, July
1988.
9. Societe Europeenne de Propulsion, Brevet Frangais 83-15263, publication 2 552 494,
1983.
10. Truchot, A., Conception et dimensionnement des protections thermiques internes d’un
propulseur a poudre, Design Methods in Solid Rocket Motors, AGARD-LS-150, 1987, pp.
1-13.
11. Yezzi, C. A. and Moore, B. B., Characterization of Kevlar/EPDM rubbers for use as rocket
motor case insulators, 22nd Joint Propulsion Conference, Huntsville, Alabama, AIAA-86-
1489, June 1986.
12. Hildreth, J. H., Advances in solid rocket nozzle design and analysis technology in the
United States since 1970, Design Methods in Solid Rocket Motors, AGARD-LS-150, 1987,
pp. 1-15.
13. Truchot, A., Conception et dimensionnement des tuyeres de propulseurs a poudre. Design
Methods in Solid Rocket Motors, AGARD-LS-150, 1987, pp. 1-27.
14. Albert, L., Nozzleless booster hardware demonstration progress to date, 24th Joint
Propulsion Conference, Boston, Massachusetts, AAIA-88-3366, July 1988.
15. Gentil, P., Design and development of a new SRM nozzle based on carbon carbon and
carbon-ceramic material, 24th Joint Propulsion Conference, Boston, Massachusetts, AIAA-
88-3366, July 1988.
16. Ellis, P. A., Testing of NOVOLTEX™ 3-D carbon-carbon integral throat and exit cones
(ITECs), 24th Joint Propulsion Conference, Boston, Massachusetts, AIAA-88-3361, July
1988.
17. Chotard, P., Ignition by shock, Proceedings Fourth international pyrotechnics seminar,
Steamboat Village, Colorado, 22-26 July 1974.
18. Sutton, G. P., Rocket Propulsion Elements, 5th edn, Wiley, New York, 1986.
19. Williams, F. A., Barrere, M. and Huang, N. C., Fundamental aspects of solid propellant
rockets, AGARDOGRAPH no. 1 16, Technivision Services, Slough, England, October 1969.
20. Timnat, Y. M., Advanced Chemical Rocket Propulsion, 1st edn, Academic Press, New York,
1987.
21. Napoly, C. and Boisson, J., Parametres d ’autopropulsion, Laboratoire de Balistique,
Sevran, no. 693, 1963.
22. Pire, Trajectoires phase propulsee, Trajectoires phase balistique, Engins balistiques et
spatiaux a propergols solides, ADERA, St Medard en Jalles, 1985.
23. Report of the propulsion and energetics panel, Working Group 17, performance of rocket
motors with metallized propellants, AGARD-AR-230, 1986.
24. Gordon, S. and McBride, B. J., Computer program for calculation of complex chemical
equilibrium compositions, rocket performance, etc., NASA LEWIS, SP-273, 1971.
25. Banon, S. and Astier, J., The contribution of inert material to end burning propellant grain
performances, 22nd Joint Propulsion Conference, Huntsville, Alabama, AIAA-86-1421, June
1986.
Propulsion Elements for Solid Rocket Motors
33
26. Thomas, A. N. Jr, The outlook for ramjets and ramjet derivatives in U. S. military
applications, AGARD Conference proceedings, no. 307, 1981, pp. 4.1-4.33. NATO Confi-
dential.
27. Marguet, R. and Cazin, Ph., Ramjet research in France: realities and perspectives, 7th
International Symposium on Air Breathing Engines, Beijing, People’s Republic of China,
ISABE-85-7022, September 1985, pp. 215-224.
28. Carri£re, P., Aerodynamique interne des reacteurs, Ecole Nationale Superieure de TAero-
nautique, Troisieme annee, Premiere partie: prises d’air, 1966, Troisieme partie: stato-
reacteur, 1965.
29. Crispin, B., Ramjet and ramrocket. Propulsion systems for missiles. Introduction and
overview, AGARD-LS-136, October 1984.
CHAPTER 2
Solid Propellant Grain Design
BERNARD ZELLER*
To design a solid propellant grain is to conceive and to define a grain which
satisfies various requirements. This chapter describes the methods and
procedures used today to design propellant grains. It describes and analyses:
• the various types of grain and the various families of propellant which are
available and used today,
• the detailed requirements that a solid propellant grain must satisfy,
• the methods which are used to precisely define the propellant, the
architecture and the configuration of the grain, and more specifically the
methods used in order to ensure required ballistic performances though
maintaining structural integrity of the grain (which is submitted to
mechanical loads all through its life),
• an overview on a method of solid propellant grain reliability assessment.
The last section comprises a more specific treatment of some special cases.
1. Introduction
During the past 20 years, requirements on performance, reliability and cost
of solid propellant rocket motors (and also on schedules and cost of
development) have become more and more stringent. This, in turn, has a
direct effect on solid propellant grain design methods and procedures, and on
development program content.
The need for improved performance is the consequence of the need for
longer ranges, higher velocities and more powerful payloads. The improve-
ment of reliability originates from the need for higher availability of weapon
systems, for lower malfunction probability and for longer service life. A
decrease of duration and cost of a development program directly reduces the
total cost of the program.
*With participation of B. Plantif, M. Vidal and M. Menez-Coutenceau.
35
36
Bernard Zeller
During the same period of time, energetic, kinetic, mechanical and aging
propellant properties have also been largely improved. Furthermore, the
power of scientific computers has greatly increased, and the use of microcom-
puters has spread widely within the project manager’s community.
Due to the pressure of competition (tactical missiles, space launchers) or
for technical/political reasons (strategic missiles), the time assigned to
designers for performing grain preliminary design* has decreased considera-
bly.
It seems appropriate to present a synthesis of the various methods used
today for designing solid propellant grains, within the larger frame of solid
propellant rocket motor design.
Design of propellant grains involves vast knowledge and numerous
techniques. This is due to the nature of propellants, the geometry and
architecture of propellant grains and to their operation modes in rocket
motors.
Grains are made of solid propellant put into a given configuration during
manufacture; their surface is generally locally restricted or inhibited (to
prevent ignition and combustion) by a flame-resistant adhesive material.
Other parts of the grain may be bonded by a liner to the motor case (case-
bonded grains).
Weights of propellant grains range from just a few grams to several metric
tonnes, chamber pressures from a few tenths to more than 30 MegaPascal
(MPa); operating times from a few milliseconds to a few minutes.
Manufacture, fielding, storage and operation of a propellant grain (within
a rocket motor) involve numerous phenomena related to chemistry, thermo-
dynamics, geometry, combustion, fluid dynamics, mechanics of continuous
media, etc. In the present chapter, it is not possible to comprehensively
analyse all the aspects of grain design which precisely define a propellant
grain which can be industrially manufactured and which must satisfy
requirements on storage and operation in various conditions. So it is
assumed that the reader is familiar with the basic knowledge of solid
propulsion (Chapter 1), internal ballistics and structural analysis (Chapters 4
and 6).
Main points discussed include:
• a description of various types of grain and associated propellants
(including French terminology);
• an analysis of requirements for solid propellant grains;
• a review of mechanical and ballistic design methods used today, particu-
larly in France;
*The result of a preliminary design is a first propellant grain definition which generally
demonstrates how initial requirements may almost totally be satisfied. Additional modifications
of the grain, often involving the use of large computer codes, are needed in order to establish the
final design.
Solid Propellant Grain Design
37
• a method of assessing propellant grain reliability;
• a description of some special designs used for very specific applications.
2. Description of Grain Geometries and
Associated Propellants
In this section, various types of grain configurations and of propellants are
presented, and also general principles on configuration and propellant
selection.
2.1. GRAIN CONFIGURATIONS
There are two main types of grain architecture: free-standing grains and
case-bonded grains. Grains of the first type are introduced into rocket motor
cases (cartridge-loaded) after manufacture. Grains of the second type are
bonded to the motor case during the casting (or injection) and curing steps of
the propellant grain manufacturing process (Fig. 1).
There is not a single, well-defined, procedure for selecting a free-standing
grain architecture or a case-bonded grain architecture for a given rocket
motor, except when one of these two architectures is obviously most
appropriate for a specific reason. Nevertheless, case-bonded grains generally
give higher performances than free-standing grains for equal available
volumes. However free-standing grains are largely widespread because this
type of architecture may present significant advantages, for instance from the
point of view of cost and of overall industrial management. Today, the trend
is toward case-bonded architectures, due to the demand for higher perfor-
mances.
2. 1. 1. Case-bonded grain configurations
When propellant grains have an outer diameter larger than 500 mm or a
weight of more than 300 kg, they are almost always case-bonded. High-
performance, middle-sized grains (outer diameter between 100 mm and
Case
Fig. 2.1. Case bonded grain.
38
Bernard Zeller
500 mm, weight between 10 and 300 kg) are case-bonded, but free-standing
middle-sized grains are very common. For small rocket motors free-standing
grains are generally used.
Case-bonded grains generally have a central port, the outer surface of the
grain is bonded by a liner (and a thermal insulation) to the motor case.
During firing, combustion of the propellant is initiated on the internal surface
of the central port and proceeds radially toward the case (and to a certain
extent longitudinally depending on the exact geometry). Exact grain geo-
metry is obtained during manufacture of the grain either by direct casting in
the case around the mandrel or by machining the port after casting and
curing have been completed.
2. 1. 1. 1. Axisymmetric configurations
AXIL : Axisymmetric grain with annular slots. The slots are circular; their
axis is the same as the grain axis. They are located all along the central port
(Fig. 2).
AXAR: Axisymmetric grain with annular slots. This configuration is similar
to AXIL, except that the slots are located near the aft-end of the central port
(Fig. 3).
CONOCYL (contraction of cone and cylinder): Axisymmetric grain with
annular slots. The tips of the annular slots are inclined toward grain head-end
so that a part of the grain is cone-shaped (Fig. 4).
Fig. 2.4. Conocyl configuration.
39
Solid Propellant Grain Design
2. 1. 1.2. Cylindrical configurations
STAR : The cross-section of the central port has the shape of an n- points star.
The contour of the star is constant along the axis [in some cases it may be
slightly tapered for manufacture practicality (Fig. 5)].
WAGON WHEEL: The cross-section of the central port looks like a wagon
wheel (Fig. 6). Numerous parent configurations exist, such as dendrite,
anchor and dogbone configurations.
Other configurations may be obtained, derived from some of the above-
described configurations. For example, bipropellant star configuration (to
eliminate sliver), or AXAR configuration having a stress-relieving annular
slot in the head-end area. Full head-end web grains are also used. Simpler
configurations such as internal-burning tube are commonly used; the ends
are usually unrestricted to function as a burning surface control; they may
also be partially restricted.
2. 1. 1.3. Three-dimensional geometries
The above-described configurations are considered as one- or two-dimen-
sional, though of course being actually three-dimensional. They are either
axisymmetric or cylindrical, with, often, an order symmetry. It is
therefore not too difficult to calculate burning area versus web burned or
stress-strain field. Today, three-dimensional configurations are becoming
more and more popular among the designer community; they are also much
more difficult to design. Most of these configurations are referred to as
Fig. 2.6. Wagon wheel configuration.
40
Bernard Zeller
“finocyl”, which is a contraction of fin and cylinder. The fins may be located
either at the head-end or at the aft-end of the grain (and sometimes at both
ends); they merge into a central cylindrical port. They may have the shape of
slots, which simplifies the geometry (Fig. 7).
Often, for stress-relieving, there are annular slots. These configurations
require three-dimensional analysis for calculating burning area versus web
burned, as well as stress-strain field or gas flow inside the central port.
2. 7. 7.4. End-burning grains
An end-burning configuration is not well adapted to case-bonded architec-
ture because of problems of structural integrity. However, it is possible to
manufacture such case-bonded grains using stress-relieving grain support
and retention systems which allow thermal shrinkage due to propellant
cooling after curing, though permitting pressure to equilibrate during firing.
2.1.2. Free-standing grain configurations
Free-standing grains are generally smaller than case-bonded grains. Be-
cause they are not bonded to the case wall, except sometimes locally, they
allow configurations which cannot be obtained with case-bonded grains (for
instance an internal-external burning tube).
Final checking of the grains is easier than in the case of case-bonded grains.
They are loaded into the motor case during final assembly of the rocket
motor. Various support systems may be used to ensure proper operation
during firing. During missile service life it is often possible, if necessary, to
replace the grain independently of other motor components.
2. 7.2. 7. Cylindrical configurations
Star, wagon wheel and tube configurations similar to those described
above may be found for free-standing grains. Grain ends are generally
simpler: they are plane and may be restricted or not. Rod and shell and
cruciform type grains may also be found.
Fig. 2.7. Finocyl configuration.
Solid Propellant Grain Design
41
2. 1.2.2. Configurations with evolving port cross-section
To reach high- volume loading fractions for free-standing grains a configur-
ation was developed: the cross-section of the central port is right circular in
the forward section and becomes progressively star-shaped in the aft section
of the grain (Fig. 8). In France this configuration is referred to as “trompette”
(trumpet), though it does not much resemble the shape of a trumpet.
2. 1.2.3. End-burning grains
The orientation of burning is totally in the longitudinal direction. This
configuration is wide-spread because gas generation rate is almost constant,
volumetric loading fraction is high and grain manufacture is easy. Side and
head faces are restricted. Burning times are long and thrust levels are low or
moderate. Thermal insulation and inhibitor play important roles, respectively,
to protect the chamber walls from the continuous exposure to hot gas and to
restrict the combustion to the desired area. They also generate pyrolysis
gaseous products during firing, which must be taken into account in the total
amount of gas generated by the grain. They are used mainly for the sustaining
phase of the flight of some missiles. Anomaly of combustion may be observed
on this type of grain, which is known as “coning”.
2.1.3. General principles for selection of grain
configuration
A practical procedure for selecting the grain configuration/propellant
combination is discussed at Section 4. Hereafter only basic principles are
discussed.
For selection of the grain configuration, the main factors which are taken
into account are:
• volume available for the propellant grain;
• grain length to diameter ratio (L/D);
• grain diameter to web thickness ratio (D/e);
• thrust versus time curve: this gives a good idea of what should be the
burning area versus web burned curve (neutral, regressive, progressive,
dual-level);
Fig. 2.8. Trumpet configuration.
42 Bernard Zeller
• volumetric loading fraction: this can be estimated from required total
impulse and actual specific impulse of available propellants;
• critical loads (thermal cycles, pressure rise at ignition, acceleration,
internal flow);
• manufacture practicality, which depends on case geometry (some grain
configurations are more or less easy to obtain);
• fabrication cost: this can be the critical factor for selecting a given
configuration.
There is no definite procedure to select a grain configuration in order to
satisfy a set of requirements, because there are often several technical
solutions to the propulsion problem.
Practically, there are some general trends in selecting configurations, based
on the shape of the burning area versus web burned curve (which is
qualitatively close to the thrust versus time curve). Table 1 summarizes these
trends. Table 2 presents the main characteristics of commonly encountered
grain configurations.
2.2. PROPELLANT SELECTION
There are several solid propellant families which differ with respect to
composition, manufacturing processes and ability to be processed into
certain configurations. These families are comprehensively presented in
Chapters 8, 9, 10 and 11.
2.2.1. Propellant families
Five families of propellants are commonly manufactured and used, and are
described more specifically in other chapters of this book.
• Solventless extruded double-base propellants (EDB); the main ingred-
ients of which are nitrocellulose and nitroglycerine. The configuration is
obtained by extrusion through a die having the desired shape. The outer
diameter is limited to about 300 mm because of equipment limitations.
Additional grain machining may be performed.
• Cast double-base propellants (CDB); the ingredients are similar or
parents to those of EDB propellants; they are obtained by casting a
mixture of nitroglycerine and triacetin into a mold containing nitrocellu-
lose-based casting powder.
• Composite modified cast double-base propellants (CMCDB), which are
derived from CDB propellants by addition of RDX, HMX, or ammonium
perchlorate and possibly nitroglycerin, in the casting powder.
• Composite propellants based on a non-energetic polymeric binder and on
ammonium perchlorate, which may also contain aluminum powder.
Table 1 Burning area neutrality versus grain configuration
Solid Propellant Grain Design
43
44 Bernard Zeller
Solid Propellant Grain Design
45
• High-energy propellants based on an energetic binder highly plasticized
by a liquid nitric ester, and on RDX or HMX, which may also contain
ammonium perchlorate and aluminum, which is called XLDB, for
“crosslinked double-base”, even if there is very little or no nitrocellulose
in the binder and a very high level of energetic solids in the formulation.
There is a terminology commonly used in France for the last three of these
propellant families, that will sometimes be used in the present book. It is
based on the following principles: the name of a propellant is made up of a
prefix, one consonant, and a suffix.
The prefix gives some information on the binder:
nitra energetic binder (usually containing nitric esters);
buta binder based on carboxy- or hydroxy-terminated polybutadiene;
iso binder based on polyurethane.
The middle letter indicates the nature of the main energetic filler.
I ammonium perchlorate;
m octogen (HMX) or hexogen (RDX);
p potassium perchlorate.
The suffix indicates the nature of the metallic fuel.
ane aluminum;
abe beryllium;
aze zirconium;
ite no metal added.
The most common of these propellants are:
• Nitramite* E:
• Isolite*:
• Isolane* :
• Butalite*:
• Butalane*:
• Nitramite* G:
Nitrocellulose/nitroglycerine binder filled with RDX or
HMX. “E” indicates that this family of propellants is
obtained through a process very similar to the one used
for manufacturing CDB propellants (known in France as
“Epictete”).
Polyurethane binder and ammonium perchlorate.
Polyurethane binder, ammonium perchlorate and alu-
minum.
Polybutadiene binder and ammonium perchlorate.
Polybutadiene binder, ammonium perchlorate and alu-
minum.
Elastomeric binder, plasticized with a mixture of liquid
nitric esters, and filled with RDX or HMX and possibly
some ammonium perchlorate. The letter G indicates that
* Trade marks of SNPE.
46
Bernard Zeller
the manufacturing process is the slurry cast (global)
process.
• Nitralane*: Elastomeric binder plasticized with a liquid nitric ester,
and filled with HMX, ammonium perchlorate and alu-
minum.
Besides the main ingredients, propellants may contain several other ingred-
ients, generally in small amounts, used as stabilizers, afterburning suppres-
sants, combustion instabilities suppressants and burning rate modifiers. One
of the important tasks of propellant designers is to find a practical way (filler,
particle size, burning rate modifier, etc.) to control burning rate, which is a
key factor in designing solid propellant grains.
2.2.2. Propellant selection
Selection of a propellant for designing a given grain is based on numerous
criteria and, here again, there is no strict procedure for selecting a given
composition. The type of architecture (case-bonded or free-standing), energy
and burning rate criteria, structural integrity considerations, smokelessness
and safety considerations, may lead toward a given propellant family. Each of
the propellant families covers a certain range of properties, and it is necessary
that the properties of the selected propellant allow design and manufacture of
a grain satisfying all the requirements. Table 3 summarizes some properties of
the main propellant families. The information presented is very succinct and
would need more thorough development. However, it allows, in combination
with Tables 1 and 2, a first approach in the selection of the couple
configuration/propellant which is detailed in Section 4.3.
3. Solid Propellant Grain Requirements
This section addresses technical requirements that propellant grains must
meet. That requirements are settled as the consequence of an agreement
between the rocket motor designer and the propellant grain designer. They
must be clear, complete and consistent, so that the propellant grain designer
may precisely define the grain and eventually build the corresponding
engineering development program.
Requirements are divided into those related to functional specifications,
those related to operational specifications and interface requirements. They
are detailed below.
* Trade mark of SNPE.
Table 3 Main characteristics of common propellants
H
a
cd
a
o
According to French regulations.
48
Bernard Zeller
3.1. REQUIREMENTS RELATED TO FUNCTIONAL
SPECIFICATIONS
3 . 1. 1 . Main internal ballistics requirements
Average, minimum and peak values of chamber pressure, thrust, total
impulse and burning times must be specified within the full operating
temperature range. Envelopes of thrust versus time or mass flow rate versus
time curves may also be specified.
3.1.2. Special requirements
Other requirements are necessary to the designer in order to define a
satisfactory propellant grain:
• Maximum weight of propellant grain.
• Maximum weight of total inert (thermal insulation, liner and restrictor).
• Maximum axial and transverse acceleration undergone by the propellant
grain during operation of the rocket motor.
• Rocket spin rate (for instance for unguided rockets).
• Dispersions on pressure, thrust, total impulse and burning time have to
be specified. Depending on the corresponding requirements, manufactur-
ing process and control operations may be strongly affected and thus the
cost of the grain also.
• Plume characteristics (emission and transmission in the visible, infrared
and electromagnetic wavelengths range).
3.2. REQUIREMENTS RELATED TO OPERATIONAL
SPECIFICATIONS
Depending on environmental conditions, definition of the propellant grain
may be significantly affected. Such conditions must therefore be well defined
in order to be correctly taken into account during the grain structural design
phase.
3.2. 1. Long-term storage
Desired maximum shelf-life, related temperature cycles and storage condi-
tions must be defined. Particular conditions (relative humidity, salty atmo-
spheres, etc.) which could directly affect propellant grain behavior must be
specified.
49
Solid Propellant Grain Design
3.2.2 . Thermal environmental conditions
The nature and number of thermal cycles undergone by missiles (for
instance during operational flights for airborne missiles) must be defined.
Generally they are the limiting factors for structural grain design because
very low temperatures may be encountered.
3.2.3. Acceleration , handling and transportation
• Acceleration before and during rocket motor operation: longitudinal
acceleration undergone by the rocket motor must be specified, as well as
radial acceleration due to rocket spin.
• Handling and transportation: dynamic loadings such as shocks and
vibrations encountered during handling (drops) and transportation must
also be specified.
3. 2. 4. Reliability
A level of reliability is more and more commonly required. It is essential to
define in which conditions it has to be satisfied. The principle of a method of
reliability assessment is discussed in Section 5.
3. 2. 5. Maintainability
The content and the planning of missiles surveillance, inspection, and
maintenance must be defined, as far as they may have an effect on rocket
motor environmental conditions.
3. 2. 6. Safety and vulnerability
These requirements are related to safety and survivability of persons and
materials. At present they are not often taken directly into account during
grain design analysis. They may induce an a priori selection of a type of
propellant (e.g. a non-detonable propellant or a propellant having a large
critical detonation diameter) or, during engineering development, the perfor-
mance of safety and vulnerability tests.
3.3. INTERFACE SPECIFICATIONS
Close environment has an important effect on grain behavior during its life
and operation. It is often prescribed by the rocket motor designer. The grain
designer must take special care that its definition is complete.
50
Bernard Zeller
3.3. 1. Case geometry and properties
A blueprint of the case, or at least its geometry (length, configuration of
head and aft-ends), is mandatory in order to perform grain preliminary
design analysis. Physical and mechanical characteristics of the case have a
direct effect on structural and ballistic design:
• type of case (metal, filament winding/resin, etc.);
• thermal expansion coefficient;
• hoop and longitudinal strains as function of internal pressure;
• maximum allowable peak pressure (depending on ultimate elastic elonga-
tion of case material);
• maximum temperature allowable at case wall at the end of motor firing.
3. 3. 2. Thermal insulations
Nature and geometry of thermal insulations (especially for case-bonded
grains) must be known in order to settle grain definition, either from a
ballistic point of view (case wall surfaces subjected to high-temperature
combustion products), or on a structural point of view (configuration of
stress-relieving fl ?s and boots). Thermal diffusivity, specific heat capacity
and mechanical ] operties data must also be available.
3.3.3. Support system
In the case of free-standing grains the support elements ensure that
combustion gas may flow between the grain and the case wall during
pressurization due to ignition. The support system must be well determined
so that prediction of grain operation may be possible at any temperature.
3.3.4. Nozzle
The characteristics of the nozzle have a dramatic effect on practical
ballistic performance of a rocket motor. The following characteristics are of
particular interest to the grain designer:
• number and orientation of the nozzles (the angle between nozzle center
line and rocket motor center line must be known);
• degree of nozzle submergence;
• erosion of the nozzle (diameter evolution) versus operation time at throat
and exit planes;
• angle of the exit cone (or a dimensioned sketch, in the case of a contoured
nozzle);
• failure pressure of the frangible closure disk (this allows definition of
ignition system and control of pressurization at ignition);
Solid Propellant Grain Design 51
• dimensions of the blast pipe (between chamber and nozzle), when
existing; this affects rocket motor efficiency.
5.5.5. Ignition system
The conditions of propellant grain ignition depend on its configuration
(location, volume, design). Important characteristics are:
• pressure at the end of ignition,
• pressurization rate (which affects structural integrity during firing).
Minimum and maximum values of delivered pressure and pressurization rate
must be accurately known because they are important factors governing
grain structural integrity. An envelope of ignition pressure versus time is of
interest for this task.
4. Ballistic and Structural Grain Design Methods
4.1. INPUT
In order to design a propellant grain, two types of data are needed:
• Technical specifications: the preceding section gives an almost complete
list of these specifications. They are the reduction of functional, opera-
tional and interface requirements that must be satisfied in order that the
rocket motor fulfill its assigned mission.
• A data bank on propellants, liners, inhibitors and thermal insulations:
this allows the grain designer to have at his disposal, quickly and with a
low probability of error, chemical, physical, kinetic, mechanical, thermo-
dynamic, etc. characteristics of the various candidate materials which
may be used in a rocket motor. The values of these characteristics will be
used as input data in analytical and computational design tools.
4.2. PROCEDURE
When performing a solid propellant grain design analysis, two levels of
design accuracy have to be distinguished:
4.2.1. First level
This is the level of preliminary design analysis. The tools used at this level
must be simple and friendly enough to be operated by propellant grain
project managers themselves. They are usually small computer codes based
on analytical models, or even graphs which give, very simply, the first results.
52
Bernard Zeller
In any case, the method involves four main stages:
• selection of a propellant/configuration couple;
• definition of grain geometry satisfying internal ballistic and structural
integrity (versus temperature cycles related loads) requirements;
• approximate assessment of erosive burning and potential combustion
instabilities;
• assessment of grain structural integrity during pressure rise at ignition.
The method is iterative: depending on the results obtained at the third or
fourth stage it allows restarting at the second or even the first stage if it
appears that the first definition needs strong modifications.
For a few years, grain designers have been requested to quickly provide
fairly precise preliminary design analysis for a given project. In order to
satisfy this request a computer-aided grain preliminary design analysis
method (MIDAP*) has been developed in France. This method is discussed
in detail in Section 4.5.
4.2.2. Second level
This is the level of final grain design. The tools required for this task are
more sophisticated. They are operated by grain design experts, and are
mainly finite differences or finite element computer codes based on two- or
three-dimensional models of physical phenomena related to internal ballis-
tics, fluid dynamics, continuous media structural analysis, etc. They allow
accurate calculations and therefore optimization of the grain final definition.
The principle of the method is parent to the one developed for preliminary
design analysis, but it starts from the final result of this analysis; that is to say
the geometry and the propellant selected at the end of the preliminary design
analysis.
Starting from this geometry, the evolution of grain burning surface area
versus web burned is accurately calculated. Taking into account propellant
properties, one obtains the evolution of chamber pressure versus time p(t\
and thrust versus time F(t). If necessary, the effect of erosive burning has to be
taken into consideration at this stage. The results must then be compared
with corresponding requirements (maximum pressure, combustion time,
total impulse, etc.). Afterwards the structural safety factor (related to thermal
cycles and pressure rise loads) must be assessed with the aid of advanced
structural analysis computer codes.
If the results are satisfactory and the design is correct, the propellant grain
definition is accepted for starting engineering development. If this is not the
* MIDAP: Methode Informatisee de Definition des A van ts- Projets (computer-aided grain
preliminary design).
Solid Propellant Grain Design
53
case, grain definition must be modified so as to increase the safety factor in
the critical grain area. Additional structural analysis must be performed in
order to check the benefits of geometry modification. Evolution of burning
area versus web burned, pressure, and thrust versus time must also be
checked so that the ballistic requirements remain satisfied. It may happen
that, after these modifications, some of the requirements are no longer
satisfied. In this event, selection of the couple propellant/geometry has to be
changed or, if there is no other possibility, modification of some requirements
has to be considered, in cooperation with the rocket motor designer.
4.3. BALLISTIC DESIGN ANALYSIS
4.3 . 1. Basic equations
Basic equations of solid propellant rocket motor internal ballistics are:
(I) p = pSV c /C D A t p = chamber pressure
p = propellant mass density
S = propellant grain burning area
V c = propellant burning rate
(II) V c = f(p) (often ap n ) C D = propellant discharge coefficient
A t = nozzle throat area
a = burning rate coefficient
(III) F = pC F A t n = burning rate pressure exponent
F = motor thrust (specific impulse
multiplied by propellant weight
flow rate)
C F = nozzle thrust coefficient
A quick examination of the basic solid propulsion equations indicates the
effects of various parameters on motor operation and therefore on motor and
propellant grain design:
• evolution of burning area versus web burned is directly connected to
pressure evolution versus time;
• sensitivity of burning rate to factors such as propellant initial tempera-
ture, rocket motor acceleration, chamber pressure, gas flow, will have an
effect on motor operation;
• p and C D , which are specific for a propellant, may be considered for
propellant selection;
• initial values, and possible evolutions during firing, of A t and C F , which
are directly related to nozzle definition (and also to propellant nature),
must be accurately known.
In the following sections, the series of stages encountered in ballistic design
analysis is described.
54
Bernard Zeller
4.3.2 . Selection of a geometry associated with a
propellant
This important part of design work has been approached in Section 2 but
only through a semi-quantitative analysis. In the present section it is
quantitatively treated using a simple method which still preserves the
designer’s judgement.
Selection is performed with the aid of charts and graphs like the one
presented in Fig. 9. The example of this figure illustrates the logical method
used, which permanently takes into account technical requirements, proper-
ties of actual propellants and characteristics of widespread actual grain
configurations. The steps are:
• Calculation of propellant mass (M p ), given total impulse (/ ft ) and
standard delivered specific impulse (7 sms ) (for an expansion ratio of 70/1
D = 160 MM
WEB THICKNESS
Fig. 2.9. Graph for aiding in critical selection of a couple propellant/geometry.
Solid Propellant Grain Design 55
and an optimum expansion ratio nozzle) measured for the propellant
likely to be selected. This first calculation is iterative, for the value of / sms
has to be corrected so as to be representative of the average conditions of
motor operation:
(a) average chamber pressure (P c ) estimated from the specified maxi-
mum pressure
(b) nozzle expansion ratio depending on maximum allowable nozzle
exit cone diameter
A s is limited by the specification on maximum diameter of nozzle exit
cone, A t equals MJP C • C D • t c , where t c (burn time) is specified.
• Assessment of volumetric loading fraction (C R ) required to obtain
specified total impulse, given the mass density of the propellant likely to
be selected and the volume available for the propellant grain.
• Selection of grain configurations. For each family of grain configuration
an empirical maximum volumetric loading fraction has been determined.
Thus, given the volumetric fraction required, one or several configura-
tions can be selected. Other criteria, such as processing practicality,
difficulty of structural analysis, propellant web thickness, have also to be
taken into consideration.
• Definition of propellant burning rate V C :V C = e b /t c .
• Verification of consistency between specific impulse, density, and burning
rate (at the average chamber pressure).
This approach must be completed by an accurate calculation of nozzle throat
diameter generating a maximum pressure lower than that required by the
specifications. This step requires a precise definition of grain geometry in
order to calculate burning area evolution which is needed for the determina-
tion of A t :
A t =
Cd * p max
On Fig. 9 the various steps of the method are represented by the path from A
to B, then to C and D, or to C and D'.
4.3.3. Calculation of propellant grain burning
area
Accurate prediction of chamber pressure evolution versus time depends on
accurate calculation of propellant burning area versus web burned. Compu-
tational tools which are commonly used belong to two families: one for “two-
56
Bernard Zeller
dimensional” configurations, the other for “three-dimensional” configura-
tions. Actual grain configurations are three-dimensional, but in numerous
cases their geometry is defined by only two coordinates (r, 9) or (r, z); in that
case, configurations are said to be two-dimensional.
4.3.3. 1. Two-dimensional geometry computer codes (Fig. 10)
These programs calculate the evolution of burning area of the following
propellant grain configurations:
• grains with a constant port area section;
• axisymmetric grains, presenting a symmetry of revolution with respect to
motor center line;
• end-burning grains with axisymmetric slots on the aft-end face.
These various codes require the description (expressed in plane coordinates)
of the initial burning area, and of every section of the propellant grain. The
computing time can be adjusted according to the level of accuracy desired.
Because of the rapidity at which the computations can be done, a visual
display of the computed burning areas is possible. As a rule the level of
accuracy is excellent. In a more complex case, where the local burning rate of
the propellant is not assumed to be independent of the curvilinear abscissa,
the evolution of the burning area as a function of time can be computed with
the help of a specially designed computerized numerical model [1].
4.3. 3. 2. Three-dimensional geometry computer codes
These codes allow the calculation of burning area of complex configura-
tions, for example finocyl grains having one or several axisymmetric slots.
One initial method, limited to the existence of a constant burning rate
Fig. 2.10. Two dimensional burning area evolution.
Solid Propellant Grain Design
57
Fig. 2.11. Initial grid of burning area.
throughout the whole grain, uses for each computation step the principle of
generation of a surface at a constant distance from the initial surface. This
software requires the generation of an initial volumetric grid with a density
suitable for the level of accuracy required in the highly three-dimensional
zones.
A grid generation can be performed only by an internal ballistics expert,
and the analysis of the evolution of the grain burning area, in spite of the
existence of grid generation preprocessed data, represents the largest amount
of work.
Another method, which allows the burn rate to be a variable function of
time and space, uses automatic grid generation and management of the
burning area evolution. The assessment of the perpendicular for each triangle
of the grid is done utilizing a numerical model using hyperbolic nonlinear
differential equations [2]. This method has allowed the development of a very
friendly software which requires only the definition of the initial grain
geometry (burning area and restricted area— Fig. 11) and parameters that
will guide the computation, e.g. level of accuracy of the results, computer
time, burning rate versus pressure law, selection of intermediary stages for
visualization, etc. (Fig. 12).
58
Bernard Zeller
Fig. 2.12. Burning surface evolution, intermediary stage.
4.3.4. Propellants burning rates
Burning rate is one of the major propellant characteristics. It is measured
on standard ballistic evaluation motors and it is stored in the data bank
mentioned earlier (Section 4.1). It is sensitive to several factors:
• Pressure . In the pressure range in which rocket motors operate, a de
Saint Robert’s burning rate law (V = ap n ) is generally preferred. It is also
possible to directly use plots of actually measured burning rates versus
pressure. The lower the pressure exponent, the more stable the rocket
motor internal ballistics.
• Temperature. Environmental and use conditions of rocket motors may
correspond to a wide temperature range. It is therefore necessary to know
burning rate sensitivity to initial propellant tempeature. It is generally
Solid Propellant Grain Design 59
expressed at a given burning surface to throat area ratio, K, as a
coefficient defined by:
where 6 is the propellant temperature.
• Acceleration. Propellant burning rate is sensitive to acceleration, but it
is taken into account only when it is more than 10 g.
• Manufacturing process. “Hump” effect is the result of change in burning
rate as a function of web burned (enhancement of burning rate in radially
burning grains in the zone between central port and motor case walls). It
is related to manufacturing process. Empirical correlations, drawn from
experience, are generally applied to take account of this phenomenon in
ballistic design.
• Internal flow. Combustion products interact with propellant combus-
tion phenomena and may locally change the burning rate law, which is no
longer the one expected. Because of the significant effect of this pheno-
menon, it is discussed in more detail in the following section.
Burning rate laws, evolution of burning surface versus web burned, and
basic internal ballistics equations provide pressure versus time and thrust
versus time evolutions. In the simple case where internal flows do not
significantly interact with burning rate, eqns (I) and (II) of Section 4.3.1,
combined with V c = de/dt , lead to a differential equation which is numeri-
cally solved and which provides web burned versus time e(t), burning area
versus time S(t), pressure versus time P(t) and thrust versus time F(t).
4.3.5. Effect of internal flows
It is often assumed that flow velocity in the central port exit plane is low
enough that it can be neglected in internal ballistics analysis. It is then
assumed that flow is accelerated only in the convergence zone of the nozzle so
that it reaches sonic velocity at the nozzle throat. In fact this assumption is
not satisfactory, because flow calculations demonstrate that velocities of the
order of 100-150 m/s are observed in the port exit plane after complete
ignition and pressurization. Depending on grain configuration and on
propellant properties, two types of phenomenon may be generated:
• a pressure drop between forward and aft-end of the central port,
• a local increase of propellant burning rate due to erosive burning.
4.3.5. 1. Criteria for occurrence of non-desired phenomena
When performing a ballistic design analysis one has to quickly assess the
magnitude of the phenomena connected with internal flow. Table 4 sum-
60
Bernard Zeller
Table 4 Intensity of phenomena due to internal flow
J
K
Erosive burning
Pressure drop
<0.2
< 50
50 to 100
100 to 150
> 150
no
yes when v < 10 mm/s
yes when v < 20 mm/s
yes; very important
when v < 10 mm/s
Low <5 %P forward end
0.2 to 0.35
< 50
50 to 100
100 to 150
> 150
no
yes when t? < 10 mm/s
yes when i? < 20 mm/s
yes; very important
when v < 10 mm/s
Approximately 10% P
forward end when J = 0.3
0.35 to 0.5
< 50
50 to 150
> 150
yes when v < 10 mm/s
yes when v < 20 mm/s
yes; very important
when v < 10 mm/s
Approximately 10% P
forward end when J = 0.4
0.5 to 0.8
< 50
and
50 to 150
> 150
yes; very important
when v < 20 mm/s
yes; very important
when v < 10 mm/s
40% ofP forward may be
observed
1
any
value
yes;
(a) very important when
t; < 20 mm/s
(b) low when
v < 30 mm/s
The pressure in the sonic
section is P cs 0.56 P
forward
marizes the knowledge empirically acquired in this field as the result of
numerous solid propellant grain design analyses. This table involves a factor
J, which is defined as:
J
K p = S'/A c
K = S/A t
A c = area of a given cross-section of central port
S' = propellant burning area upstream of the above cross-section
S = propellant grain burning area
A t = nozzle throat area
4.3.5 2. Pressure drop
Pressure drop is related to a decrease of pressure from grain head-end to
grain aft-end. It induces an increase of head-end pressure at the first phase of
Solid Propellant Grain Design 61
motor firing, and therefore maximum pressure generally increases. Pressure
drops are generally due to:
• energy losses inside the flow, and to phenomena occurring at the interface
of flow and propellant surface or to sharp changes of port section or of
flow direction,
• side injections from burning propellant walls.
One of the critical steps in rocket motor operation therefore occurs just after
ignition when port sections (through which combustion gas must flow) are
minimum. Average pressure drop values encountered are of the order of
0.1 MPa between head- and aft-end. In some cases, for special configurations,
pressure drops of more than 1 MPa have been observed.
A gaseous flow is fully characterized by the knowledge of local velocities
and pressures. Computer codes have been developed in order to determine
such characteristics; they are named PROCNE 2 and PROCNE 3 (depend-
ing on whether geometry is respectively two- or three-dimensional). They
allow:
• description of unsteady phases during pressure rise at ignition,
• calculation of steady flow just after ignition, in the whole cavity and in the
nozzle convergence section.
In order to use these codes one has to generate a grid of the combustion
chamber. Order “n” symmetry (when existing) is taken into account so as to
reduce the analysis to a sector of 2n/n (n = symmetry number). Figure 13
presents an example of a grid created inside the cavity of a finocyl propellant
grain having a symmetry number of 32. Results may be presented either as
gas velocity or pressure field (Fig. 14) or as curves representing, for instance,
gas velocity as a function of radial distance to the central axis in central port
cross-section.
4.3. 5. 3. Erosive burning
Enhancement of propellant burning rate due to tangential gas flow
(compared to propellant burning rate without tangential flow) is known as
erosive burning. It occurs when the propellant burning surface is subjected to
Fig. 2.13. Three dimensional flow inside rocket motor, grid of central cavity.
Fig. 2.14. Three dimensional flow inside a rocket motor: velocity field (Mach number of the flow).
Solid Propellant Grain Design
63
a high-velocity combustion gas flow parallel to it. The phenomenon is due to
an increase of heat transfer from the flame zone to the propellant surface.
There are numerous physical models to explain and to quantify this
phenomenon [3]. Practically, a simple computer code (COMBEROS), based
on a monodimensional flow model, allows the calculation of the head-end
and aft-end pressure evolution in a grain experiencing erosive burning. The
erosive burning law selected for the model is:
K = V 0 U + a(G - G 0 )]
V e = burning rate with erosive burning;
V Q = burning rate without erosive burning;
G = mass flow rate unit in the given port cross-section;
G 0 = mass flow rate unit threshold (beyond which erosive burning occurs).
Both a and G 0 are obtained empirically.
The COMBEROS code is used systematically in preliminary ballistic
design analysis. It implies that grain geometry can be described by the cross-
section contour perimeter evolution along the grain axis. Erosive burning is
calculated in several cross-sections of the central port according to local flow
characteristics (static pressure P and local mass flow rate G) and to the above
erosive burning law. The ignition phase is simulated as an unsteady pheno-
menon; time steps range from 1 to 5 ms. A complete motor firing may be
simulated, using a steady-state model and time steps generally ranging from
0.05 to 0.1 s (Fig. 15). A more comprehensive investigation of erosive burning
64
Bernard Zeller
in propellant grains, though keeping a one-dimensional geometry assump-
tion, may be performed with a more sophisticated code [4].
4.3.6. Combustion instabilities
Grain design must incorporate an assessment of combustion stability
during motor firing. The phenomenon of combustion instability may occur
when perturbations excite oscillation modes of the chamber cavity. Inter-
action with combustion, flow, particles, nozzle, etc., may induce either an
increase or a decrease of the phenomenon. When it increases, pressure
vibrations and pressure increase may consequently be driven to an unaccept-
able level. In order to assess combustion stability, a two-step procedure is
followed [5].
Pressure inside the combustion chamber cavity is assumed to be:
— = £ e 0,, 'e JK>, '4' ; (M)
Po 1 = 1
p 0 = average chamber pressure;
p' = instantaneous pressure at point M;
c o t = pulsation of mode of rank i and of frequency /■;
i = spatial form of mode of rank i ;
M = point in grain cavity;
a* = damping coefficient (when oc f < 0), or gain factor (when a f > 0) of the
mode of rank i.
The first step of the analysis consists in calculating the various acoustic
modes specific to the grain cavity. A finite-element two-dimensional com-
puter code, VASAX, is used. An example of a two-dimensional grid and the
corresponding results are presented respectively in Figs 16 and 17 (the rank
of the mode is 3).
Fig. 2.16. Combustion instabilities: grid of a motor cavity for calculation of acousti-
cal modes.
?? ???? s
rra
csjr-o
do'doo dob oooo
Fig. 2.17. Combustion instabilities: pressure contour lines.
Solid Propellant Grain Design
65
The second step of the analysis consists of calculating the value of a. These
calculations need not only the results of the first step, but also data describing
propellant response to pressure, effect of condensed particles, etc. The
computer code AVER is used.
Depending on the value of a (equal to the algebraic sum of the various gain
and damping factors), it is possible to evaluate the grain propensity to
experience combustion instabilities: for a mode of frequency f h a value of a f ,
larger than 0.1 f t indicates that there is a significant probability that
combustion instability may occur. The grain configuration (or propellant)
has to be modified.
4.4. STRUCTURAL DESIGN ANALYSIS
4.4. 1. Principles of structural design analysis *
Various loads are imposed on propellant grains throughout their lifetime,
from their manufacture until motor firing. These loads depend not only on
the rocket motor’s own characteristics but also on manufacturing tempera-
ture, environmental and operational conditions. Various factors affect loads
imposed on a grain (especially a case-bonded grain):
• curing temperature;
• acceleration of gravity;
• type and number of thermal cycles undergone during storage and
transportation (for instance captive flights for airborne missiles);
• acceleration during boost phase;
• pressurization during grain ignition.
The goal of structural analysis is to calculate a safety factor defined as:
where C is the propellant (or bond) structural capability (allowable), and S is
a function related to stress/strain induced in the propellant grain region
undergoing the more severe loads (margin of safety may be defined as C — S
or C/S — 1). In order to compare them, C and S must be of the same physical
nature.
The safety factor must be higher than 1 during the rocket motor lifetime,
including motor firing. According to this definition it is assumed that grain
cracking or propellant/liner debonding induce significant modifications to
rocket motor internal ballistics having consequences ranging from failure of
This section may use notions developed in Chapter 6.
66
Bernard Zeller
missile mission to rocket motor explosion. It is assumed that failure at the
most stressed (strained) point does not depend on the stress (strain) gradient
in the surrounding region.
If the safety factor calculated for a given propellant grain and given
imposed loads is lower than the required value, the propellant grain system
has to be redesigned until a satisfactory safety factor is obtained.
Assessment of capability variations (due to manufacturing process, to
material reproducibility, to mechanical testing, to aging, etc.) and of induced
stress/strain variations (due to uncertainties of boundary conditions, im-
posed loads and stress/strain determination methods) allows, as a result of a
probabilistic analysis, estimation of reliability of a series of propellant grains
of a given definition. This subject is discussed in Section 5.
The procedure followed in order to predict safety factors comprises two
major aspects: it must define how to assess propellant and propellant-liner
bond structural capabilities on one hand, and how to determine induced
stress/strain in various loading conditions encountered by the grain, on the
other hand. This procedure is schematically presented in Fig. 1 of Chapter 6
of this book.
Propellant and propellant-liner bond capabilities are determined by
performing various mechanical tests and require a failure criterion which is
defined as the critical value (at failure) of a function related to the state of
stress (or strain) of propellant or bond.
Determination of induced stress/strain involves a structural analysis
requiring input data such as geometry, boundary conditions (e.g. case
displacement), and propellant and bond mechanical behavior.
Results are expressed using the same function selected for failure criterion
so that they may be directly compared to propellant and bond capabilities.
Experimental validation of the procedure has to be performed, either on the
propellant grain itself or on subscale analogs, whenever new elements — such
as uncommon grain configurations, new propellants or new bonding sys-
tems— have to be considered in safety factor assessment.
4.4.2, Assessment of structural capabilities and
of mechanical behavior
Propellant or propellant-liner bond capability is the maximum mechanical
loading which can be imposed on the propellant or the bond before failure
occurs. Capability is determined by performing tensile (and other) testing on
various specimens. The main parameters affecting propellant and propellant-
liner bond capability are:
• loading rates (which are very different when thermal cooling or pressuri-
zation at ignition have to be simulated);
• temperature;
• surrounding pressure (when simulating ignition pressurization).
Solid Propellant Grain Design
67
As a whole, the experimental work performed on this subject has led to the
conclusion [6-8] that propellant behavior is:
• viscoelastic, as evidenced by relaxation tests;
• nonlinear, although considered linear for small deformations;
• Incompressible (Poisson’s ratio is very close to 0.5), until dewetting is
significant enough to cause volume variations during tensile testing.
The function which expresses propellant capabilities is described in Section
4.4.4.
4.4.3. Determination of induced stress /strain
fields
The determination of induced stress/strain fields in the propellant grain
requires a knowledge of:
• geometry on which loads are imposed;
• boundary conditions which describe imposed loads;
• propellant and propellant-liner bond behavior.
In most cases the geometry is three-dimensional, loads are static, dynamic or
thermally induced and propellant behavior is viscoelastic and nonlinear.
Loads which are the limiting factors in structural grain design are generally:
• thermally induced, in the case of grains for tactical missiles (low-
temperature cycling);
• pressurization-induced, in the case of grains for large ballistic missiles
(stored in almost isothermal conditions).
At the preliminary design phase the expected maximum value of stress/strain
induced in the grain is quickly assessed using analytical expressions. For
instance, in the case of fairly simple internally perforated grains, the following
expressions are commonly used:
e = 2a- AT -K { -C-(b/a) 2
for a thermally induced strain.
£ is the equivalent strain at the grain inner bore surface;
a is the propellant thermal expansion coefficient (assumed to be at
least an order of magnitude higher than the case material
thermal expansion coefficient);
AT is the difference between stress free temperature and temperature
at which induced strain has to be estimated (A T may be as large
as 100°C);
K { and C are corrective coefficients taking into account respectively cen-
tral port exact geometry and end effects;
b and a are respectively grain outer and inner radii.
68
Bernard Zeller
In the case of a pressurization-induced strain,
e = k-E 0s -p-K r C-(b/a) 2
e 6s is hoop strain of the empty case submitted to ignition maximum
pressure;
/? takes into account case stiffness increase due to propellant grain;
k is an empirical coefficient.
These values of e are input data for a first assessment of the grain safety factor.
The final design phase involves extensive use of computational methods
based on finite-element techniques applied to grain stress/strain field analysis.
The procedure comprises three stages:
4.4.3 . 1. The determination of the induced stress/strain field
This assumes a linear behavior for the material. The stress/strain field is
governed by the incompressible behavior of practically all of the propellant
grain.
The mechanical load establishing the boundary conditions is expressed
either as prescribed displacement, or as prescribed forces at the nodal points
of surface elements. Several different computer analysis programs, either two-
or three-dimensional, may be used for this phase.
A typical program will have the following characteristics:
• Finite-element method.
• Quadratic elements with 20 nodal points.
• Quadratic surface elements with eight nodal points to allow accurate
assessment of stress/strain at the surface of the grain. The use of surface
elements increases the accuracy by dramatically reducing the uncertain-
ties caused by the fairly loose extrapolations necessary to calculate
maximum stress/strain when there are no skin elements.
• HERRMAN reformulation on incompressibility.
The level of accuracy of the results is a function of the precision of the grid
generated to represent the geometries. The number of nodal points must be
limited because of computer capacity and CPU time. A typical grid will
include 7000 nodal points and 1000 elements.
Figure 18 shows an example of a two-dimensional grid.
4.4.3. 2. Post-processing analysis
The assumption is made that the propellant behavior is linear and
incompressible. The regions of the grain where the stress/strain is the greatest
are identified. Figure 19 gives a three-dimensional grid example with stress
contour lines for equal stress. The maximum stress occurs, in this case, at the
forward slot bore junction.
Solid Propellant Grain Design
69
Fig. 2.19. Three dimensional grid network.
70 Bernard Zeller
4. 4.3. 3 Determination of stress/ strain in the regions
experiencing the greatest induced load
Starting with the above results, the determination of strain/stress in the
most highly loaded regions is refined by introducing a viscoelastic nonlinear
model for thermally induced strain/stress, and an elastic nonlinear model for
pressure-induced stress at ignition.
(a) Thermally induced load
The structural model used is a viscoelastic nonlinear model. It provides, at
any moment of an imposed thermal cycle, the values of the principal stresses
in the propellant (cr lth , cr 2th , a 3 th)- The numerical method used is incremental
with respect to the time, the principles consists in calculating stresses at a
given time t from the values known at time t — At. For that purpose, the effect
of the thermal cycles are handled as successive stresses with simultaneous
relaxation of the stresses observed at the preceding time [9].
The results of this program have been compared many times with the
results of tests performed on propellant grains. The program itself is
continuously being improved.
(b) Pressurization-induced stress at ignition
This structural model requires propellant master curves and data charac-
teristics of the pressurization (pressure rise time, final pressure, temperature).
It provides the values of the main stresses (cr lp , cr 2p , cr 3p ) corresponding to the
maximum pressure.
When performing a structural analysis of a propellant grain at the time of
firing, which occurs after the effect of a thermal cycle, the maximum stresses
will be determined by adding the principal stresses resulting from the
thermally induced stresses and pressure-induced stresses, provided that the
principal directions for both stresses are identical. This is true for external
surfaces, where the most stressed areas are frequently located.
4.4.4. Determination of structural safety factor
At the stage of preliminary design analysis, simple analytical formulas
provide the magnitude of strain either due to thermal loading or due to
pressure rise (see Section 4.4.3.). In both cases, propellant capability is
obtained from the master maximum strain curves at t/a T corresponding to
the loading conditions. So a first assessment of the safety factor is:
_ £ (due to thermal loading or pressure rise loading)
e m (at t/a T corresponding to the loading conditions)
71
Solid Propellant Grain Design
Propellant capability (Section 4.4.2.) is related to uniaxial tensile tests; it is
represented by maximum stress (cr m ) or maximum strain (e m ). Induced stress
(strain) (Section 4.4.3.) is the result of a stress (strain) analysis; it is expressed
as principal stresses (a l5 a 2 , a 3 ) (strains, £i,£ 2 ,£ 3 ) * n the most severely
stressed (strained) region of the grain.
In order to be able to directly compare capability and induced stress
(strain), failure criteria are needed [10]. They are based on an equivalence
between principal stresses and an equivalent uniaxial stress defined by:
Von Mises criterion
g 0 = [(o-i - <j 2 ) 2 + (a 2 - C7 3 ) 2 + (a 3 - <r 1 ) 2 '] ll 2 /a 112
or
Stassi criterion:
g 0 = [(^1 + Gj + C7 3 ) + [(ff! + <7 2 + cr 3 ) 2
+ b\Xa ! - a 2 ) 2 + (<t 2 - (S3) 2 + (o 3 - <7i) 2 ]] 1/2 ]/c
a, b , c are coefficients which generally depend on the propellant, but do not
depend on strain rate and temperature.
According to the magnitudes of (<r l9 a 2 , ^ 3 ), it is either the Stassi criterion
or the Von Mises criterion that is used. The Stassi criterion is used mainly in
the case of thermally induced stresses, and the Von Mises criterion is used
mainly for pressure-induced stress at propellant grain ignition (ignition at
7 Mpa). The parameters of the induced pressure on the propellant grain to
determine these criteria are obtained experimentally by performing tensile
tests under atmospheric and various other pressures, at various temperatures
and stress rates.
The propellant grain safety factor is then defined as the ratio of the
maximum stress (obtained in a uniaxial tensile test performed at the strain
rate and temperature equivalent to those applied to the grain) to the principal
maximum uniaxial stress (obtained from the failure criterion, either from
Stassi or from Von Mises criteria, depending on the type of stresses
encountered in the most stressed region of the grain), equivalent to the
maximum three-dimensional state of stress calculated in the propellant grain:
jor _ S m (t/a T )
9 ~ MS, VM)
The safety factor may also be defined as:
K e m (t/flr)
e e 0 (S, VM)
Where £ 0 is the ratio of equivalent uniaxial stress to the modulus.
72
Bernard Zeller
There are other methods to predict safety factors; these are discussed in
Chapter 6, Section 6. In addition, an analysis of most of these methods was
recently published [11].
In the case of propellant liner bonds the problem is a different one because
of the presence at all points of the interface of two different materials— the
propellant and the liner. The tensors representing stress/strain on both sides,
propellant grain and liner, are different. Only the force applied to the
interface is continuous. Its components are: a perpendicular strength, (7 n , and
a shear strength, t. The safety factor is determined by comparing the modulus
of interface strength (components a n and r) to the modulus of the interface
force at the time of failure, obtained under identical conditions on a
propellant liner bond specimen.
In most cases the propellant liner bonds are designed for failure to occur in
a propellant grain area close to the interface. Furthermore, should the
propellant in this area have the same properties as the bulk of the propellant,
the safety factor will be calculated the same way, and:
^bond min.[/C s trength at bond’ ^propellant!
4.5. COMPUTER-AIDED PRELIMINARY DESIGN OF
PROPELLANT GRAINS
4.5. 1 . General description
As mentioned in Section 4.2., there is an increasing pressure to have, as
early as the preliminary design phase, quick and relatively accurate results
defining the propellant grain. Moreover, further changes in technical require-
ments need to be easily taken into account. A computer code satisfying these
needs is now on service. It is named MIDAP [12] and it involves, today,
around 20,000 statements in its newest version. Figure 20 presents the general
architecture of the code. Each type of grain configuration (star-shaped,
slotted tube, axisymmetric, finocyl, etc.) is individually treated inside the
code. The procedure for any of these configurations is the one which is
generally followed to perform propellant grain preliminary design analysis (it
is described in Section 4.2.). The architecture of the code is modular so that
any addition of a new module, or any improvement of an existing module,
may be very simply worked out.
Runs are controlled by the user from the graphic terminal. CPU time is
negligible as compared to time spent by the user performing the design
analysis.
The process is iterative and, besides the input of technical specifications,
the user has only to answer yes or no to the option proposed on the screen.
Results are presented either as tables or as curves. The block diagram
Solid Propellant Grain Design
73
Fig. 2.20. General structure of preliminary design analysis computer code.
presented in Fig. 20 emphasizes the role of propellant/configuration selection,
which provides several possibilities, ranked according to a given set of
criteria. The selection of propellant/configuration depends:
• on the one hand, on technical requirements (total impulse, burning time,
etc.);
• on the other hand, on semi-quantitative requirements related, for in-
stance, to manufacturing process practicality, industrial and economical
aspects, etc.
Due to the dual nature of the criteria, an expert system was selected and
implemented for this critical stage of preliminary design analysis.
4.5.2. Description of the code
All the branches of the code have the same basic structure. The slotted tube
branch is detailed below. On the flow chart of Fig. 21 the main stages of the
analysis appear. Two possibilities are provided to the user:
• design of a case-bonded (or free-standing) grain meeting technical
requirements;
• for a given rocket motor, calculation of motor operation (pressure versus
time, thrust versus time, etc.).
In the case of slotted tube configurations, geometrical characteristics which
are taken into account for design analysis are:
• cylindrical motor case, presenting possibly thermal insulation overthick-
ness in the aft-end zone (slotted zone);
74
Bernard Zeller
Fig. 2.21.
• plane grain aft-end zone (slotted zone);
• cylindrical central port;
• slot walls may be parallel or not (star-shaped);
• possibility of a tapered port in grain aft zone (in order to limit erosive
burning effects).
The successive steps of the analysis are:
• First definition of the grain and thermal structural analysis. This defini-
tion meets various requirements, the priorities of which are ranked as
follows:
(1) Structural integrity (for thermally induced strains) corresponding to
a safety factor higher than 2.
Solid Propellant Grain Design
75
(2) Maximum operating pressure.
(3) Total impulse.
(4) Evolution of pressure versus time.
(5) Burning time.
The structural analysis is based on data obtained from regression analysis
of stress/strain field determination results, performed with the aid of
three-dimensional computer codes on various selected slotted tube
geometries.
• Burning area evolution. This task is performed by dividing the grain into
three parts as described in Section 4.3.3.
• Determination of nozzle throat initial diameter. This is the minimum
throat diameter value consistent with the specification on maximum
acceptable pressure.
• Determination of pressure, mass flow rate and thrust evolutions versus
time. In a first approach, erosive burning is not taken into account. The
calculations provide expansion ratio, and thus nozzle optimum expan-
sion ratio and exit diameter. Nozzle exit diameter is then compared to
corresponding requirement. Afterwards, ratios K (burning area to nozzle
throat area) and J (burning area to central port cross-section) are
calculated. If needed, a tapered zone is designed in the grain slots region
so as to meet a criterion on J (maximum permitted value). Burning area
versus time is then calculated again.
• Definition of equivalent axisymmetric longitudinal port contour. This is
based on equal flow rates in any port cross-section for actual (three-
dimensional) and equivalent (two-dimensional axisymmetric) contours.
It allows a simplified analysis of erosive burning which is taken into
account at the following stage.
• Calculation of head-end and aft-end pressure evolution. At this stage,
erosive burning is taken into account. The module provides pressure
evolution inside grain central port, as well as peak pressure at ignition
and pressure rise time.
• Prediction of safety factor related to ignition pressurization. Preliminary
structural design analysis is performed, as described in Section 4.3.3.
5. Propellant Grain Reliability
Reliability is the probability that a system will fulfill a required mission in
given conditions and during a given period of time. Reliability must be
considered:
• at the design phase— the system must be designed so that its reliability
will meet the requirement;
• at the realization phase— it must be demonstrated that the reliability
requirement has been met.
76
Bernard Zeller
Reliability of a solid propellant rocket motor results from the reliabilities of
constitutive elements, such as case, thermal insulation, igniter, nozzle, propel-
lant grain, etc. Grain reliability has several components; but main compo-
nents are ballistic and structural reliability. In the case of case-bonded grains,
past experience and analysis performed according to FMECA (failure modes,
effects, and criticality analysis) have demonstrated that structural reliability is
the most important component of overall grain reliability.
There are two possible approaches in assessing propellant grain reliability:
an analytical approach and an experimental approach; both of them are
complementary.
5.1. ANALYTICAL APPROACH
This is performed according to the FMECA method [13]. It consists of:
• listing the functions the propellant grain must fulfill;
• describing failure modes;
• assessing probability of failure occurrence for each mode;
• validating assessments by comparing with overtests and analog experi-
mental results.
As mentioned above, this method places emphasis on the structural compo-
nent of case-bonded grain reliability. This aspect is therefore discussed below.
A comprehensive description of the methods used in propellant grain
structural reliability assessment would need extensive discussion because of
the complexity of phenomena and analytical tools involved. Consequently,
the following section provides only an idea of the principles governing
structural reliability assessment.
Safety factors are considered in Section 4 as having known values:
propellant grain failure occurs when K = C/S = 1. K is the structural safety
factor, C is capability and S is induced stress/strain. In fact, most of the
parameters involved in safety factor prediction are randomly distributed and
their statistical distribution law is not always well known. These parameters
are related to:
• grain geometry
• boundary conditions
• propellant and bond behavior
• capability
• failure criterion
which define induced
stress/strain field,
which may take aging
into account,
When designing a case-bonded grain the distribution law of the parameters
defining grains and imposed loads must be known, so that the distribution
law of C and S can be known. It is then possible to determine the minimum
safety factor ensuring required reliability. In a second stage, taking into
account variations due to manufacture (and possibly to aging), it is possible
Solid Propellant Grain Design
77
to define a mean safety factor (higher than the preceding one) that must be
the objective at the design phase. Grains designed so as to meet this
requirement on K have the desired reliability at a high confidence level.
For a given propellant grain, variations of capability and induced stresses
(strains) are due to:
• errors in test measurements of propellant and bond mechanical proper-
ties,
• the probabilistic nature of loads imposed to the grain before, and during
firing,
• uncertainties related to structural models and to failure criteria determi-
nation.
Let C and S be the mean values respectively of capability and of induced
equivalent stress (strain) and CV c and CV S corresponding deviation factors
(which are assumed to be independent of the mean value), then K = C/S , and
it can be demonstrated that the probability that grain failure does not occur
is:
Prob(C > S) = ®[ {K 2 CV 2 + ^1/2]
where <t> is the repartition function of normal distribution law. C and S are
generally assumed not to be correlated (which is not correct but acceptable).
It is possible, however, to take a correlation into account if it is clearly
demonstrated.
Minimum safety factor, K min , ensuring required reliability F, is then
obtained by determining the value of K min which satisfies the relationship:
(K 2 min CV 2 + CV 2 ) 112
Taking into account variations due to manufacture, deviation of the safety
factor is assessed. It is then possible to calculate a value of safety factor which
is the objective of structural design analysis: it ensures that grains accordingly
designed have a given probability of meeting the reliability requirement.
5.2. EXPERIMENTAL APPROACH
Safety margin is C — S. There is a discrepancy between actual margin of
safety (C — S) R and predicted margin of safety (C — S) c , due to the use of an
approximate model. It is possible to write (C — S) R = (C — S) c + £, where £
is assumed to obey a normal distribution law. The £ mean value, m^,
represents the shift of the model. Deviation represents variations of this
shift; m ( and must be assessed by performing significant experimental tests.
There are two possibilities: either overtests or tests on grain analogs.
78
Bernard Zeller
5.2.1. Overtest
The first method is to assume that £ obeys a given normal distribution law
and to use overtest results in order to refine this distribution law: this is the
Bayesian method [14]. Grain overtests are tests which have a moderate
probability (much higher than in a normal motor firing or temperature
cycling) that failure does occur. Much information is thus obtained on grain
reliability. Overtests are defined by changing thermal cycles applied to the
grain (colder temperature, larger cycles number) or firing conditions (reduced
nozzle throat diameter) compared to normal conditions.
The most interesting information is obtained when overtest performance
does not induce propellant or bond failure: a more accurate definition of
distribution law may thus be proposed.
5.2.2. Tests on grain analogs
A second method to quantify the shift of the model consists in performing
loading tests on analogs [15]. This analog grain has the following character-
istics:
• configuration is simple enough so that analogs may be easily manufac-
tured at low cost;
• two-dimensional geometry induces low-cost computational structural
analysis;
• the ratio of maximum stress (strain) to mean stress (strain) induced in the
analog is of the same order of magnitude as the one encountered in actual
grains;
• maximum induced stress (strain) can be easily adjusted by simply
modifying analog manufacture tooling.
The main drawback is that the analog is not ... the grain itself, which means
that propellant, liner and bond are not exactly the same, and are not in the
same surrounding conditions as those constitutive of the actual grain.
Mechanical testing consists in loading a given number of analogs in
identical conditions until failures occur. Analysis of failure results and
deviations yields the shift ^ between actual margin of safety and predicted
margin of safety. It is then assumed that the shift observed on the analogs is
equal to the shift existing in actual grains.
This set of complementary theoretical and experimental methods allows
the assessment of structural reliability of case-bonded solid propellant grains.
6. Special Cases
Probably over 90% of cases encountered in practice are included in the
preceding discussions. There are, however, some special applications that do
Solid Propellant Grain Design
79
require special configurations or designs, such as: (1) segmented propellant
grains; (2) nozzleless grains; and (3) wired, end-burning grains. Finally, an
additional special grain, designed to reduce the base drag of shells, is
discussed in Chapter 8 and is the special topic of integral boosters in Chapter
12.
6.1. SEGMENTED PROPELLANT GRAINS FOR SPACE
LAUNCHERS
The need to launch objects with ever-increasing weight revealed the
necessity for rocket motors capable of very high levels of thrust and total
impulse at the beginning of the launching operation, to provide the energy
needed for lift-off, and to traverse the thick layers of the atmosphere under
very precise conditions of acceleration. This has led to the design of special
rocket motors. During the first 2 minutes of flight they may deliver a thrust 10
times greater than the thrust of the central rocket motor. The required thrust
levels are found within the operating ranges of solid propellant grains, so that
solid propellant rocket motors are a basic complement to the classic liquid
fuel of these launchers [16].
These rocket motors are positioned on the periphery of the central liquid
fuel motors, requiring a very high ratio of length to diameter, that can be as
high as 10; the propellant grain may weight over several hundred tonnes.
It is therefore very difficult to manufacture a rocket motor of this type in
one single monolithic assembly in classic manufacturing facilities designed
usually for the production of propulsion stages for ballistic missiles. The
manufacture of these rocket motors turned toward assembling several
sections, called segments. Each of these segments consists of several tens of
tons of propellant grain case-bonded in a section of metallic case. The
segments are then assembled to reproduce the classic configuration of a case-
bonded propellant grain [16,17]. Figure 22 shows a four-segment configura-
tion. As a rule, one segment has a star-shaped configuration providing a
greater impulse at lift-off, for approximately 20 seconds.
The particular characteristics of these types of propellant grains are the
burning areas on the end faces of the segments, resulting in high gas flow rate
in the proximity of the joints.
The thrust curve is controlled by working on the star-shaped configura-
tion, the taper coefficient of the central port and the restriction of head-end
surfaces by inhibitors.
The general criteria used for the geometry design, and other methods
discussed in the preceding sections, are for the most part applicable. A certain
number of specific problems must, however, be resolved:
80
Bernard Zeller
6. 1. 1. Acoustics
The head-end burning areas, at the segments’ interface, can produce radial
flows disturbing the central gas flow. These disturbances may cause instabili-
ties in the gas flow. This type of situation is similar to axisymmetric
propellant grains with radial slots. In addition, the exposure of the inhibitors
during the burning process may cause pulsations in the gas flow and be the
source of additional acoustic energy [ 18 ].
6.1.2. Segment assembly
The segments are connected to each other, and the motor cases are
assembled together through a system of clamps and pins.
Sealing of junctions is ensured by flexible seals. These junctions must be
protected against the presence of combustion gas in the intersegments during
the ignition phase. These junctions are one of the weak points of the rocket
motor. The difficulty comes from the stress/strain imposed on the junction
during pressure rise at ignition, and from the difficulty of inspecting this area
after assembly.
6. 1.3. Rocket motor pairs
There are at least two boosters located on the outside of the launcher.
Consequently, closely matched thrusts from each specimen are necessary to
allow good control of the flight, and particularly to avoid any troubles at
separation at burn-out.
Solid Propellant Grain Design
81
Thrust imbalance between boosters is usually the result of variations in the
burning rate of the propellant grain, but may also be caused by other factors
linked to the nozzle (erosion, etc.).
Control of thrust imbalance is obtained through adjustment of the
ingredients, the manufacture process, and control method [1].
6.2. NOZZLELESS BOOSTERS
The nozzleless booster is an early design that resulted from an analysis of a
classic rocket motor, demonstrating that the nozzle accounted for a signifi-
cant portion of the cost, weight and size of a rocket motor.
The propellant grain of a nozzleless booster is usually case-bonded with a
generally cylindrical central port, connected at the aft-end to an exit cone
tailored in the propellant.
In the absence of a nozzle throat, the operating conditions of the nozzleless
rocket motor are governed by an aerodynamic constriction of the gas flow.
The exit cone section at the aft-end of the grain is designed to allow gas
expansion.
The development of nozzleless rocket motors is linked to composite
propellants with high burning rates, because this type of propellant grain
requires a minimum flow rate to ensure a stable performance, in turn
requiring prohibitive length-to-diameter ratios when other propellant com-
positions are used.
The main advantages of nozzleless rocket motors are:
• simplicity of the propellant grain geometry,
• greater loading ratio than in a conventional rocket motor,
• weight reduction, due to absence of mechanical parts at the aft-end and
absence of nozzle,
• significant decrease of the cost of the rocket motor,
• performance improvement for a given size,
• elimination of a nozzle which otherwise would have to be ejected at the
end of the acceleration phase, making this concept very interesting for use
as an integral booster for rocket ramjet systems [4].
There are some drawbacks as the price to pay for these advantages:
• loss of approximately 20% of specific impulse in comparison to a
conventional system [19];
• the possibility of occurrence of combustion instabilities at low pressure;
• the need to have a thorough knowledge of the normal burning rate and
erosive combustion for a very large range of pressures, to enable
performance predictions [20];
• the propellant grain mechanical deformation directly reflected in the
ballistics of the motor [21].
82
Bernard Zeller
A highly regressive combustion pressure curve is a characteristic of a
nozzleless rocket motor operation, reaching very low pressure (Fig. 23).
Because of these particular operational characteristics, the design analysis of
a nozzleless rocket motor can be performed only with very specific computer
models.
All of these models are monodimensional, a typical code using a single-
phase, quasi-stationary description of the flow. The precision of the calcula-
tions depends on a very exact knowledge of propellant grain combustion
laws, as well as an exact description of the geometry of the structure and the
grain’s central port, including structural strains.
Before undertaking the computer analysis, and in order to limit computer
time, the following method may be used to perform a preliminary design
analysis:
• limit the minimum central port diameter for structural integrity reasons;
• in the case of a given diameter, determine the required length of the
propellant grain by using J s of approximately 215 seconds for Butalane
and 200 seconds for Butalite.
• determine the diameter of the central port, for a given maximum pressure,
using the following simplified formula [22]:
D = 4pLC* v{p)
0.8 ’ p
p = maximum pressure;
v(p) = burning rate at maximum p;
p = density;
C* = characteristic burning rate;
L = estimated length of the propellant grain.
Fig. 2.23. Typical thrust-pressure curves of a nozzleless propellant grain.
Solid Propellant Grain Design 83
These preliminary values for the diameter and the length are used in the
computer analyses to optimize the propellant grain.
6.3. WIRE END-BURNING GRAIN
The concept of the wire end-burning free-standing propellant grain first
appeared at the beginning of the 1960s. Wire end-burning is one of the means
available to increase the effective burning rate of a propellant grain and, in
addition, it is particularly well suited for a high loading ratio of the rocket
motor. It is based on a simple observation: the burning rate along a wire
embedded in the propellant grain is faster than inside the propellant grain
itself [24].
Consequently, the burning surface is modified by the formation of a cone
whose vertex travels along the wire. Its half-angle at the vertex is solely a
function of the ratio between the propellant grain’s specific burning rate and
the burning rate along the wire. The overburning rate coefficient N is
calculated as follows:
K wire = burning rate along the wire;
V = propellant burning rate;
a = half-angle of the cone.
This phenomenon is linked to a modification of the thermal field next to the
wire, and is a function of the nature and diameter of the wire as well as the
nature of the propellant. The principle is used to increase the gas flow rate of
front-end burning grains by placing continuous, straight wires, perpendicular
to the initial burning surface.
The preliminary analysis of the performance of this type of propellant grain
involves two distinct steps that cannot be handled using traditional means:
• The determination of the overburning rate coefficient of a given wire/
propellant combination. Currently, this determination is mostly experi-
mental. Theoretical approaches are being developed, requiring the gener-
ation of a complete data base for thermal data on wires and on
propellant, e.g. diffusivity, conductibility, thermal capacity, etc.
• Determination of the evolution of the wire grain burning surface. When
dealing with front-end-burning propellant grains the computational
programs are relatively easy to generate, since the evolution of the grain’s
burning surface involves nothing but cones. The difficulties increase with
the number of wires embedded in the propellant grain.
84 Bernard Zeller
Bibliography
1. Delanoy G. and Loubere, B., A physical method for predicting thrust imbalance of solid
rocket motor pairs for a satellite launcher AIAA 87-1740, AIAA/ASEE/SAE/ASME 23rd
Joint Propulsion Conference, 1987.
2. Leroux, A. Y., Ribereau, D. and Namah, G., Numerical model for propellant grain
burning. Conference on mathematical modeling of combustion and related topics. Ecole
Centrale de Lyon, 1987.
3. Razdan, M. K. and Kuo K. K., Erosive burning of solid Propellants. Fundamentals of solid
Propellant, Combustion Progress in Astronautics and Aeronautics, Vol. 90, pp. 515-598, 1984.
4. Delannoy, G., Prediction of antitank solid propellant rocket internal ballistics. AIAA-84-
1355. AIAA/SAE/ASME 20th Joint Propulsion Conference, 1984.
5. Philippe, A. and Tchepidjian, P., Prediction of longitudinal combustion instabilities in
axisymmetrical propellant grains. AIAA-84-1358. AIAA/SAE/ASME 20th Joint Propulsion
Conference, 1984.
6. Farris, R. J., Development of solid rocket propellant nonlinear viscoelastic constitutive
theory. AFRPL-TR-75-20, 1975.
7. Francis, E. C. et al. Propellant nonlinear constitutive theory extension. Preliminary results.
AFRPL-TR-83-034, 1983.
8. Lhuillier, J. N. et aL, Tenue mecanique et fiabilite des chargements a propergol solide.
Sciences et Techniques de I'Armement, 52, 11-144, 1978.
9. Meili, G., Dubroca, G., Pasquier, M. and Thepenier, J., Etude mecanique de chargements
moules-colles en propergol double base composite par une methode viscoelastique non-
lineaire. Propellants, Explosives, Pyrotechnics , 7, 78-84, 1982.
10. Tschoegl, N. W., Failure surfaces in principal stress space. Polymer Science Symposium, 32,
239-267, 1971.
11. Wang, D. T. and Shearly, R. N., A review of solid propellant grain structural margin of
safety prediction methods, AIAA-86-1415. AIAA/ASME/SAE/ASE 22nd Joint Propulsion
Conference, 1986.
12. Uhrig, G., Durourneau, B. and Liesa, P., Computer aided design of propellant grains for
solid rocket motors. AIAA 87-1734. AIAA/ASME/SAE/ASE 23rd Joint Propulsion Confer-
ence, 1987.
13. L’analyse des modes de defaillance, des effets et des probability. Cahiers de securite de
rUnion des Industries Chimiques. Cahier No. 4, Paris, 1981.
14. Quidot, M., Methodes d’incorporation de resultats d’essais a la mesure de la fiabilite. Note
technique interne No. 98-77-CRB, 1977.
15. Thepenier, J., Menez-Coutenceau, H. and Gondouin, B. Reliability of solid propellant
grain; mechanical analog motor design and testing. AIAA 87-1987. AIAA/SAE/ASME 23rd
Joint Propulsion Conference, 1987.
16. Vidal, M. and Varl, E. Les chargements a poudre des propulseurs deceleration d’Ariane
5. Aeronautique et Astronautique, 123, 122, 1987.
17. McDonald, A. J., Evolution of the space shuttle solid rocket motors— something old or
something or something new. AIAA 85-1265. AIAA/SAE/ASME 21st Joint Propulsion
Conference, 1985.
18. Brown, R. S., Dunlap., R,, Young, S. W. and Waugh, R. C., Vortex shedding as an
additional source of acoustic energy in segmented solid propellant rocket motors. AIAA 80-
1092, AIAA/SAE/ASME 16th Joint Propulsion Conference, 1980.
19. Procinsky, J. M. and Smith, W. R., Nozzleless Boosters for Integral Ramjet Systems.
AIAA/ASEE/SAE/ASME 16th Joint Propulsion Conference, 1980.
20. Traineau, J. C. and Kuentzmann, P., some measurements of solid propellant burning rates
in nozzleless motors. AIAA 84-1469, AIAA/ASME/SAE/ASEE 20th Joint Propulsion
Conference, 1984.
21. Munday, J. W., Mikeska, A. J. and Tomkin, M. E., N.P.P. Grain deflection model. AIAA
82-1201, AIAA/ASEE/SAE/ASME 18th Joint Propulsion Conference, 1980.
22. Nahon., Nozzleless solid propellant rocket motors. Experimental and theoretical investiga-
tions. AIAA 84-1312, AIAA/ASME/SAE/ASEE 20th Joint Propulsion Conference, 1984.
23. Atlantic Research Corporation, Perfectionnements aux grains propulseurs. Patent No.
1349125, 26 September 1961.
24. Caveny, L. H. and Glick, R. L., Influence of embedded metal fibers on solid propellant
burning rate. Journal of Spacecraft, 4 , 1, 1967.
CHAPTER 3
Prediction and Measurement
of Specific Impulse
JEAN-PAUL BAC
1. Introduction
In the previous two chapters the importance of specific impulse has been
noted several times.
All new propellant formulation research, or preliminary design analysis of
a solid rocket motor, assumes knowledge of a theoretical value for specific
impulse whence it is possible to start the analysis and give a direction to the
research.
In most cases, calculations of the theoretical value of the specific impulse
are performed with the assistance of thermochemical computations. The
principal algorithms which are used throughout the world come from a
computer program developed at the Lewis Research Center of NASA [1].
This chapter is a succinct description of the process, to allow the reader to
understand the sequencing of the main phases of calculations to create a
model for the gas and condensed phase* mixture from the combustion
chamber to the exit plane of the nozzle.
Such models lead to solution of a system of equations with partial
derivatives as a function of time and spatial coordinates [1-3]. The calcula-
tions themselves require access to the JANNAF thermochemical tables.
These tables were first issued in 1971 and are periodically updated [4].
The purpose of Section 2 is to present and discuss a very simplified model,
based solely on thermodynamics. It is specifically designed to provide an
approximate value for the main operating parameters of a rocket motor
without having to solve a differential equations system.
The application of the model to obtain predictions, followed by the
experimental method for the measurement of the specific impulse, is dealt
* Condensed phase = combustion products in solid or liquid state.
85
86
Jean-Paul Bac
within Sections 3 and 4. The chapter ends with a discussion of special
application to performance predictions for solid fuels for ramjets.
N.B. The thermodynamics values used in this chapter are written as
follows:
• Italic capitals: characteristic values of the overall system.
• Script capitals: molar values.
• Italic lower case: values per unit of mass.
2. Physical Model
2.1. DESCRIPTION OF THE MODEL
Physical phenomena associated with rocket motor combustion and flow
processes are complex; it is therefore necessary to use a model based on an
ideal motor, operating under a number of simplifying assumptions, to
perform the required calculations.
More specifically, the combustion in the chamber is assumed to be
adiabatic, at constant pressure, and yielding to a mixture of ideal gases and
condensed phase products that are incompressible with a negligible molar
volume in comparison with the gases. In addition, this mixture is in
thermodynamic equilibrium at zero velocity. The combustion is followed, in
the nozzle, by an isentropic flow, steady and quasi-one-dimensional, during
which the condensed phases remain in thermal and kinematic equilibrium
with the gas.
The assumption of steady flow allows us to work on the basis of per unit
mass values.
The thermodynamic condition of adiabatic equilibrium maximizes entropy
while observing the law of conservation of matter. Because we are assuming a
transformation under constant pressure and at zero velocity, conservation of
enthalpy ( h ) also occurs. With constant pressure and enthalpy, maximizing
entropy is equivalent to minimizing Gibbs free energy:
g = h — Ts.
The use of the various assumptions given above allows us to progressively
build a system of equations which, when solved, provides the values of the
major operating characteristics of an ideal rocket motor.
2.1.1 . Conservation of mass
For each of the elements of the chemical species included, we can write:
05
fri = z a ii n i = b h i=Ut
j=i
( 1 )
Prediction and Measurement of Specific Impulse
87
where:
£ = number of elements;
ns = number of species;
a t j = number of atoms of element i in a species of type j (a species is a given
chemical compound or element in a given physical phase);
Hj = number of moles of these species in the mixture;
= number of atom-grammes of element i in the propellant grain.
2 . 1.2 . Minimizing free energy
Using the Lagrange multipliers linked to these equations, this condition
is written as:
n = ( dg/dtij)T , p, {n k ; k #;'} = £ j = 1, ns (2)
i = 1
where g is the free energy per kilogram of mixture, T the gas temperature, and
p the pressure.
Writing gases from 1 to m and the condensed products from (m + 1) to ns
( = m -h nc\ (where nc stands for the number of condensed species), we have:
fij = fi°j(T) + RT In njn + RT In p/p°; j = l, m (2a)
Pj = p°j(T ); j = m+l,ns (2b)
• pj is the free molar energy (or thermodynamic potential) of the pure j
species, in the same physical state (solid, liquid or gaseous) as the phase
where this species is found in the mixture, under standard atmospheric
pressure p° and at the temperature of the mixture.
• n is the total number of moles in the gaseous phase:
m
n = Z n i ( 3 )
j= i
2. 1.3. Enthalpy conservation
With j as the molar enthalpy of species j and h the enthalpy per unit of
mass of the propellant grain, we can write:
ns
h= X njjr o j(T) = h 0 (4)
j= i
When p is known, we have a system of (1 + ns + 2) eqns (l)-(4) with
(1 + ns + 2) unknown [(2 t ), (h,-), n and T].
This system is perfectly defined and can therefore be solved, and it is
possible to calculate the entropy at equilibrium s.
88 Jean-Paul Bac
2. 1.4. Isentropic expansion
This assumption enables us to write:
ns m
S = X tij if] (T) - R X ttj In tijp/np 0 = s 0 (5)
j = 1 j~ 1
• Sfj the molar entropy of the pure species j, under standard atmospheric
pressure p°, in the same physical state (solid, liquid or gaseous) as the
phase where this species is found in the mixture, and at the temperature of
the mixture;
• s 0 the entropy per unit of mass in the chamber.
Two types of calculations are performed:
• expansion at thermodynamic equilibrium;
• expansion in frozen composition
In both cases the system is determined by the knowledge of the pressure.
In the first case we have a system of (1 + ns -f 2) eqns [(1), (2), (3) and (5)]
with (1 + ns + 2) unknowns [(2^, ( rij ), n and T], and in the second case one
eqn (5) with one unknown T.
Consequently, we can calculate the mass per unit volume p = p/nRT , the
enthalpy h (T) per unit of mass, the coefficient of isentropic expansion
y s = (5 In p/d In p\ and the velocity of sound:
a(T,p) = y/y s nRT
2. 1.5. Steady-state expansion
With v , the combustion gas velocity, we can write:
v 2
h + H = h o
(6)
i.e.
V = y/2 (h 0 - h)
(6')
The sonic throat of the flow is defined by:
v — a
(7)
The throat pressure ratio is determined through iterations on the pressure
calculation, starting with the combustion pressure ( p 0 ).
2. 1. 6. Assumption of a one-dimensional linear
flow in the exit cone
Indices x, s and t designate, respectively, any cross-section of the divergent
part of the nozzle, the section in the exit plane of the nozzle, and the section at
Prediction and Measurement of Specific Impulse 89
the throat of the nozzle. The equation of the conservation of mass is written
as:
Mstfs = M A = p t A t v t
( 8 )
It is therefore possible to:
• either select a value for the ratio of sections e = AJA t and calculate the
exit conditions with iterations on the pressure;
• or select the exit pressure and calculate the other parameters, including
the sections ratio.
Using the various assumptions above, it is possible to write the equations
required for the thermodynamic calculations and hence obtain the data that
characterize the flow of gases and condensed products.
These data are then used to calculate the parameters characteristic of the
operating point of the perfect motor. For example, the value of v s obtained
from eqn (6') can be used for either of the following purposes:
• either the calculation of standard adjusted expansion with p 0 = 7 MPa
and p s = p a = p° = 0.1 MPa, obtaining the standard specific impulse
Is = ”s/0O'
• or the calculation of expansion in a vacuum at given s and obtaining the
specific impulse in a vacuum / vac = vjg 0 + pjp s v s g 0 .
If the values of A s and A, are also selected, in addition to the values of e, we
can calculate:
• the mass flow rate: m = v s A s p s
• the thrust: F = mv s + (p s — pJA s
The following are also calculated:
• The flow rate, or discharge coefficient:
^ rh _ P, • v t
— A —
Po A t Po
• The characteristic velocity:
C* = 1/C D =
P „•/*,
rh
P 0
Pt-»t
C F —
F
Po ’ A{
h ’ Cd * Go
• The thrust coefficient:
90
Jean-Paul Bac
2.2. LIMITATIONS OF THE MODEL
2.2. 1. General assumptions
The thermodynamic model used is concerned only with the area related to
the propellant gas volume, whose characteristics are calculated in the
combustion chamber and then during the expansion in the nozzle.
We have to apply the laws of macroscopic physics and chemistry: the
conservation of mass, the principles of dynamics, the first law of thermody-
namics, the law of thermodynamic state, and laws of chemical kinetics and
physical kinetics of changes of state. These laws were written for closed
systems with the presence of physical equilibrium, which is not the case with
the open system to which we are applying them. This is tantamount to
considering the gas as closed subassemblies under physical equilibrium, i.e.
considering the flow to be much more “orderly” than it really is. The gain
in entropy is thereby underestimated; consequently, the mechanical effi-
ciency — i.e. the impulse — is overestimated.
The amount of this overestimation cannot be predicted. This oversimplifi-
cation must be done, unless all interactions between the atoms were to be
written and integrated within the whole motor.
It is assumed that the gas is neither viscous nor heat-conductive (and
consequently, that the phenomenon is adiabatic), and that the condensed
products stay in thermal and kinematic equilibrium with the gas.
This assumption is not absolutely essential to do the calculation, but it
simplifies it greatly. It also results in an overestimation of the impulse, which
is particularly significant when the propellant produces condensed products.
There is, indeed, a thermal and kinematic disequilibrium between the
condensed products and gas, the latter being both more rapid and less hot
than the condensed products.
The adiabaticity assumption, a corollary of the non-conductivity of the
gas, also leads to an overestimation of the thrust. This is particularly true
when the motor is small and not very well insulated.
In spite of the reservations listed above, this set of assumptions allows us to
write eqns (1) and:
• The global equation for the conservation of mass:
dp/dt + p div v = 0 (9)
• The equation for the fundamental law of dynamics:
py + grad p = 0
( 10 )
Prediction and Measurement of Specific Impulse
91
• The equation for first law of thermodynamics:
v 2 \
u+ l)
dt
+ div p ■ v = 0
( 11 )
u = the internal energy per unit of mass of the combustion product.
• The equation of state:
P = P(T, p, {ny, j = l, ns})
( 12 )
• The kinetic laws:
dn
= nj(T, p, {n k }; k #7); j # j, (13)
The number of eqns (13) is equal to the number of species, less the number
of elements in their standard state, i.e., (ns — 1).
Equation (10) is a vectorial equation that corresponds to three differential
equations. We therefore have a system of (6 + ns) differential equations with
(6 + ns) unknowns v x , v y , v z9 T, p, p and {n y }.
2.2.2. Assumption related to the combustion
chamber
First it is assumed that the gas velocity, and consequently the pressure
gradient, is negligible in the combustion chamber. This approximation is
reasonably well justified, particularly in the case of a large motor operating at
low maximum pressure.
It is further assumed that gases in the entry plane of the nozzle are in
thermodynamic equilibrium. This assumption is consistent with the previous
one. It is also fairly well justified, particularly in the case of a large, well-
insulated motor.
These are the two assumptions used to calculate initially an equilibrium at
constant pressure at zero velocity in the combustion chamber.
2.2.3. Assumption related to the gas expansion
The flow is considered to be isentropic. This is not a good assumption since
an actual flow is by nature irreversible, and therefore non-isentropic, if it is
adiabatic. This particular assumption contributes greatly to an overestima-
tion of the impulse. As for solving the equations, it enables the creation of a
relation independent of time and spatial coordinates, between the number of
moles, the temperature and the pressure. But it is of no interest if it is not
complemented by an assumption which enables us to by-pass equations of
92
Jean-Paul Bac
chemical kinetics (13). It explains (but does not justify) the decision to
perform two calculations, one in thermodynamic equilibrium and the other
in which the composition remains unchanged. All other assumptions being
equal , the truth lies somewhere in between, closer to equilibrium in the
convergent part of the nozzle and closer to frozen composition in the
divergent part of the nozzle. Expansion in thermodynamic equilibrium
overestimates the impulse, while expansion assuming frozen composition
underestimates it.
Using these two complementary assumptions (isentropic flow and thermo-
dynamic equilibrium, or frozen composition), the choice of a pressure
determines the temperature and the composition of the mixture.
We then assume a steady-state flow. This assumption is justified by the fact
that we are generally looking to obtain an operation which stays quasi-steady
during the major portion of its duration. This assumption contributes to an
overestimation of the impulse inasmuch as, all other assumptions being
otherwise identical, steady-state specific impulse is always greater than
specific impulse which is calculated including the pressurization and burnout
phases.
Under this steady-state flow assumption (9), the equation reads:
divpv = 0 (14)
Combining eqns (14) and (11) gives:
d l h +
d t
At
= 0
(15)
The quantity ( h + v 2 /2) is therefore constant along a streamline. Since all
flow lines start from the entry section of the nozzle, we can write:
h +
2
— K
(16)
2.2.3. 1. Analysis of the conditions at the throat of the nozzle
With a steady flow the location of the sonic throat of the flow is stable. It is
located at the actual geometric throat of the nozzle.
Equation (14) can then be replaced with
v = a
to determine, iteratively, the pressure at the throat.
The transformation of propellant into gas is accompanied by an increase in
volume. Combustion produces a gas with a velocity v c , such as:
_ AV _ 1 dV dm _ 1 /I _ 1\ .
V ° S dt S dm dt S p p ) m
Prediction and Measurement of Specific Impulse
93
where:
p c = mass per unit of volume of the gases inside the combustion
chamber;
p p = mass per unit of volume of the propellant grain;
v = volume of the propellant grain;
s = burning area of the propellant grain.
Our steady combustion assumption requires that we neglect l/p p before \/p c
and write:
m = p p Sv r = p c Sv c = p t A t v t
where v r is the burning rate of propellant grain for a pressure p Q in the
combustion chamber.
If velocity v r is known, the burning area to throat area ratio K = S/A t can
be determined, and by iterations on the pressure of the chamber, the burning
rate at which a steady operation should occur can also be determined.
2.2.3. 2. Analysis of the conditions in the divergent part of the
nozzle
Using previous assumptions (adiabatic, isentropic and steady expansion,
in equilibrium or with frozen composition), the knowledge of the pressure at
one point determines the temperature, the composition of the mixture, and
the velocity of the flow at that point.
To simplify calculations an unrealistic approximation is made, for model-
ing this segment of the nozzle: the pressure is assumed uniform over any
nozzle cross-section, and, consequently, that the velocity is everywhere
parallel to the axis.
Therefore, the equation for the conservation of matter is written as
PsA»s = Px A xPx = PtM
Because of that, the following results are obtained, in a cross-section:
• a pressure and mass per unit of volume which are constant for the entire
cross-section rather than increasing from the periphery to the center;
• a velocity which is constant for the entire section instead of decreasing
from the center to the periphery (v instead of v cosine a, oc being the half-
angle at the apex of the divergent part).
As a result, this approximation:
• leads to an overestimation (all things being otherwise equal) of the ratio
of cross-sectional areas necessary to obtain fixed expansion;
• contributes to the overestimation of the impulse by an amount that
cannot be exactly determined, although it is known to be of the order of
(1 — cosine a), and therefore of about 1%.
94
Jean-Paul Bac
Finally, in order to analyze what occurs in the exit section of the diverging
part of the nozzle, it is necessary to research the interaction of the jet with the
merging air stream. This problem is far more complex, and resolving it is
completely out of the question. The assumptions necessary to bring its
complexity down to the level of the preceding assumptions would completely
change its characteristics. We therefore limit ourselves to:
• Assuming that p s = p a for an expansion at a given ambient pressure, and
then calculating the corresponding cross-sectional area ratio. However, p s
is necessarily greater than p a because the velocity can be different from
zero in a given direction only if the pressure diminishes along the
corresponding streamline. But this difference is very small, because the
ejected gas molecules have an infinite expansion volume, so that they are
in an infinitesimal minority compared to the merging air stream and the
velocities resulting from intermolecular collisions rapidly become ran-
dom. This simplification does contribute to an overestimation of the
impulse, although to a much less important degree than with the
preceding assumptions.
• Calculating p s regardless of p a , for a given expansion ratio.
If p a has been determined to be much greater or smaller than p s , the impulse
calculated will have no significance, because there probably will be no steady
operation with such a pressure mismatch.
If p a is determined to be a little less than p s , then the entire set of
assumptions is self-consistent, and provides a specific impulse with a good
indicative value.
2.2.4. Conclusion
In conclusion, the specific impulse calculated using this model is always
overestimated. The smaller the rocket motor, the higher mass fraction of
condensed phase material elements in the combustion gases and therefore the
higher this overestimation. With a propellant producing no condensed
phase products the overestimation will be highest if the combustion gas
viscosity and thermal conductivity are higher. (For a propellant grain
producing condensed products, there are combinations of viscosity and
conductivity for which the overestimation is minimal, all other assumptions
being equal.) It is necessary to have a value of this overestimation to
determine the average specific impulse of rocket motor. A range of values is
found in Chapter 1.
The specific impulse determined in this manner provides mainly a compar-
ative value. Even then, great caution is required since, disregarding the size
factor, the deviations between the calculated and the actual specific impulses
depend on the intrinsic characteristics of the propellant, i.e.
Prediction and Measurement of Specific Impulse 95
• its physical structure, which plays a major role in the degradation
mechanism;
• its basic composition and the molecular structure of the chemical
components, which determines its enthalpy, its free energy, its reaction
mechanism in the gaseous phase, and the ballistic characteristics (isen-
tropic ratio, viscosity and thermal conductivity) of the combustion gases.
Since each one of these characteristics plays a special role in the deviations
between the actual specific impulse and its calculated value, there is no reason
to believe that ratio ‘7 S predicted versus / s actual” will be identical for all
propellants. It is more accurate to state that this model offers the possibility
of a valid classification of the propellant within a particular family, and also
for propellants with the same molar ratio of condensed products. But caution
is advised when comparing two different propellant families. Since the
deviation between the actual specific impulse and predicted value is of the
order of 10% for any one propellant, a calculated difference of 4-5% between
families of propellant is not necessarily meaningful.
3. Predictions
Specific impulse predictions are commonly used in two main areas:
• new propellant formulation research;
• determination of the theoretical performance of a rocket motor.
3.1. NEW FORMULATION RESEARCH
Technical requirements such as guidance and low signature, related to the
mission of the missile (particularly in the tactical area), affect the selection of
the propellant. In addition to highest performance, the designer must also
look for formulations with combustion gases that provide, for example:
• No absorption of electromagnetic waves required for missile guidance.
This absorption is caused by the ionization of the gases, particularly
alkaline or alkaline-earth.
• No absorption in infrared — another factor in guidance — which sup-
poses aluminum contents lower than 0.5%.
• No absorption in the visible range, to avoid detection of the missile,
requiring a plume containing no condensed elements and without any of
the HCl-type gases, i.e. gases that can condense when combined with
molecules of the atmosphere (H 2 0 in this case).
The calculated results include the cheminal compositions of the plume,
allowing its classification according to the established characteristics for
operational requirements.
In addition, when identifying the optimum composition from a family of
96
Jean-Paul Bac
propellants, a parametric analysis is performed using the three major
components (for example, the binder, ammonium perchlorate and alu-
minum). A ternary diagram is drawn (Fig. 1). Studying the curves / s , T c , or
P'I S — constant allows the selection of the highest performing propellant
composition., Although a large number of complete calculations are required
for these diagrams — approximately 30 for each propellant family — they are
very frequently used. They afford substantial savings in cost and research
time by limiting the number of experimental tests that would have to be
performed for such a selection.
3.2. DETERMINATION OF THE THEORETICAL PERFORMANCE
OF A ROCKET MOTOR
Based on the technical requirements of a rocket motor, total impulse: I Ft,
combustion duration, dimension and on the theoretical specific impulse
selected, the calculations related to the ballistics (Chapters 1 and 2) also allow
the identification of an average operating point (e, p 0 , pj.
Fig. 3.1. Theoretical specific impulse diagrams (seconds).
Prediction and Measurement of Specific Impulse 97
The previously defined thermochemical computations are typically pro-
grammed for computer solutions. Using results from such a computation, the
preliminary analysis designer is able to calculate the theoretical performances
of the rocket motor. In addition to the values of the specific impulse (fixed
nozzle expansion and expansion to vacuum), he can also obtain the exact
composition of the plume as well as the thermodynamic values (C p , y, /i, M,
H,S ) which characterize the system.
These values will be used as entry data to calculate the flow in the
combustion chamber (Chapter 4), or the loss of performance in the nozzles
(Chapter 1).
The thermochemical computations are also used to predict the theoretical
performance of more complex chemical systems, such as:
• rocket motors using end-burning propellant grains for which the gases
from the erosion of the thermal insulation and inhibitors must be taken
into account with the combustion gases of the propellant grain [6];
• ramjets using solid fuels for which the mixing of combustion gases with
air needs to be calculated (Section 5 of this chapter).
4. Measurement of the Specific Impulse
4.1. INTRODUCTION
Whether determining the value of the specific impulse of a propellant or of
any rocket motor, this prediction requires:
• the use of test facilities designed for the purpose (firing stand);
• the acquisition of all data (pressure, thrust, time, mass, etc.) with a
maximum of precision;
• a very exact description of the methods used to interpret the results.
The following section describes the equipment necessary to perform the tests,
as well as the various operations performed, using as an example the
prediction of the standard specific impulse of a propellant.
4.2. THE THRUST STAND
The thrust stand must be capable of withstanding and accurately monitor-
ing the full thrust developed by a rocket motor. There are various types of
firing benches, including:
• the blade bed,
• firing beds with sliding plates,
• vertical benches,
• pendulum gun,
• spinning benches.
98
Jean-Paut Bac
The blade bed is most widely used to determine the characteristics of a
propellant by firing standard configuration propellant grains. It is shown in
Fig. 2; the rocket motor is attached to a very rigid frame suspended from rigid
supports with a set of flexible blades. The role of the blades is strictly limited
to that of a mechanical linkage, having no impact whatsoever on the thrust
measurement. They must not be too flexible, to avoid parasite vibrations
resulting from ignition of the rocket motor.
The thrust of the rocket motor is transmitted to a load cell.
The continuity of the load cell is completed by a pre-load screw which is
attached to a block of solid concrete that absorbs the thrust of the motor.
The bench construction must be done carefully to ensure a perfect
alignment between the thrust axis of the rocket motor and the axis of the cell.
Fig. 3.2. Test bench.
Prediction and Measurement of Specific Impulse 99
4.3. THE STANDARD MOTOR AND HEAVY WALL MOTOR
This is the test motor configuration used to determine the average
standard specific impulse (/ sm ). The description given in this section is related
to the French standard. This equipment is specially designed for repetitive
tests necessary when the measurements taken are for the control of industrial
production, or for development analysis. For the latter, the metal parts are
over-sized, and those parts that have not been heavily exposed to combustion
gases (front end and the cylinder) can be reused with a limited amount of
maintenance work. On the other hand, because of the importance of their
definition for the precision of the measurements, certain subassemblies
(nozzle throat, exit cone) are systematically replaced.
The complete assembly includes three major parts:
(1) An end base, equipped with a rupture disc to limit the pressure in case
of a problem during combustion. The pressure and thrust cells are
attached to the base. Thermal insulation is placed in the inside of the
motor.
(2) The propellant grain which is contained in a cylinder for cartridge
landing (this may also be insulated).
(3) A cylindrical part, where the free-standing propellant grain is placed.
This may also be thermally insulated.
(4) A rear assembly, made also of three parts: a convergent section, or
nozzle, a nozzle throat, and a divergent section (Fig. 3).
Concerning the convergent section of the nozzle:
• it is made of a heat-resistant material (composite or graphite material);
• the half-angle of the convergent section is 45° — the diameter at entry is
equivalent to the diameter of the free-standing propellant grain;
100 Jean-Paul Bac
• no discontinuity is permitted in the convergent section of the nozzle,
including at the junction with the throat the nozzle;
• the surface must be as smooth as possible.
Concerning the throat of the nozzle:
• it is usually made of graphite;
• the radius R of the junction where the convergent and divergent portions
meet is such that R> 0 throat;
• the diameter of the throat is a function of the size of the free-standing
grain, of the composition of the propellant, and of the desired pressure.
Concerning the divergent section:
• it is very often made of composite material;
• the half-angle of the divergent part is 15°;
• the exit diameter is calculated as a function of the desired expansion.
4.4. THE PRESSURE TRANSDUCERS
• Two types of pressure transducers are used on the motors.
• Piezoelectric sensors with a broad frequency response to allow detection
of rapidly changing combustion phenomena.
• Strain gauges to provide very precise measurements of the steady-state
pressure curve.
4.5. THE PROPELLANT GRAIN
The selection of the propellant grain configuration is based on the
following criteria:
• The burning area should have little dependence on the web burned so
that the pressure as a function of time resembles a step function (instant
rise, constant pressure plateau, instant pressure drop) as must as possible.
• The evolution of the grain burning surface should be as predictable as
possible, which requires:
(a) a constant burning rate along the central port, devoid of any
interfering phenomena such as erosive burning, or combustion
instabilities (Chapter 4), and
(b) a very precise knowledge of all configuration characteristics, in
particular the thickness of the web and the mass of the propellant
grain.
• Fabrication should be simple and reproducible to reduce production
costs.
• The mass of propellant should offer a good compromise between a value
sufficient to limit errors related to measurement (weight, dimensions, etc.)
and a value that respects the previous criterion.
Prediction and Measurement of Specific Impulse 101
A large number of types of propellant grains fulfilling these criteria are in use
throughout the world. The more detailed description that follows is limited to
two of the propellant grains often mentioned in this book.
4.5.1. The star-shaped central port propellant
grain
This propellant grain, called MIMOSA as used in France, has a star-
shaped central port with 10 segments. Its outer diameter is 203 mm; its
weight is approximately 45 kg for 1 m of length. It has been used for a long
time as a control propellant grain for the ballistic properties of composite
propellants.
The neutrality of the burning grain surface evolution,
c _ c
^max ^min
C
^average
as a function of web burned, is very good.
The star shape, however, has the drawback of generating a burning surface
area evolution which, as it evolves into the final phase (starting at the
moment when the burning area is bordering the case), causes a pressure drop
with a small combustion tail-off.
For research on new propellants the size of each sample propellant grain is
kept small. This minimizes cost and enables evaluation of a large number of
compositions. Another propellant grain called CAMPANULE may be used.
Its weight is much lower (2.5 kg), with a 90 mm diameter and 300 mm length.
It has a star-shaped central port, 10 segments, and provides initial data on the
levels of specific impulse. Different companies or organizations use cylindri-
cal smaller grains.
4. 5.2. Perforated grain [7]
This is a propellant grain with a circular central port with flat, uninhibited
end surfaces. This type of propellant grain, used in the United States, is
known as the BATES (Ballistic Test Evaluation System). The burning area
versus web burned is very constant, with no combustion tail-off: the pressure
decrease at burnout is only controlled by the venting of the combustion
chamber.
This propellant grain is available in several different sizes, as shown in
Table 1. The 7-inch and 12-inch sizes are used in France to determine the
characteristics of energetic binder compositions (Chapter 2) because of the
very good tail-off curve. This is important for these formulations with high
pressure exponent at low pressures which can lead to unbumed residual
propellant with other initial surfaces.
102
Jean-Paul Bac
Table 1 Main characteristics of the various BATES propellant grains
Outside diameter
(inches)
Length
(inches)
Approximation propellant mass (kg)
7
12
6.5
12
20
35
28
60
380
4.6. MEANS OF MEASUREMENT
The measurement system must faithfully record the strain/stress signals
given by transducers during the motor firing. The analog processing of the
signal is not very precise, so a digital processing is usually preferred. A classic
measurement system is shown in Fig. 4.1.
4.7. DETERMINING THE PARAMETERS OF A FIRING TEST
{N. B . : The exact definition of the parameters, as well as the equations used,
are found in Chapter 1.)
This section involves the calculation, for a given propellant grain composi-
tion and type, of the three types of parameters discussed below.
4.7. 1. Operating pressure of the firing test
The ideal, of course, is to reproduce standard operating conditions
(expansion ratio 7/0.1, Chapter 1), which alone legitimize comparisons of
Fig. 3.4. Measurement system.
Prediction and Measurement of Specific Impulse 103
performance between various propellant grains. Consequently, the average
value of pressure obtained during the firing test should be 7 MPa.
This value is representative of the operating range of most of the composite
propellants (approximately 3-11 MPa), and will therefore be selected for the
firing test parameters used in MIMOSA and BATES configurations.
Some double-base propellants differ, and have an operating range between
approximately 15 and 30 MPa. They require a pressure corresponding to the
plateau of their burning rate versus pressure curve (Chapter 9). These test
conditions necessitate correction of the measurement data to obtain a final
value that corresponds to the standard conditions.
4 . 7 . 2 . Dimensions of the nozzle throat and of the
exit plane
The diameter of the throat of the nozzle is calculated as follows:
Cd-Po' a t = p-S-v
where:
C D = propellant discharge coefficient;
p 0 = combustion chamber pressure;
A t = area of the throat,
p = mass per unit of volume of the propellant grain;
S = burning area of the propellant grain;
v = burning rate of the propellant grain at pressure p Q .
The diameter of the divergent part of the nozzle (exit plane) is calculated as
follows: using the throat diameter, and the section ratio e = AJA { (ratio of
the area of nozzle exit plane versus the area of the throat), we can determine
the diameter of the exit plane. This ratio is a function of pressures p 0 and p s ; it
also varies according to the value of for the propellant gases (Chapter 1). The
thermodynamics calculations done for the propellant yield a value such that
the pressure in the divergent exit plane is equal to the ambient atmosphere
pressure.
In the case of aluminized propellants, when the test firing occurs with a
chamber pressure in the range of 7 MPa (expansion ratio of gases p Q /p s is 70),
that value is of the order 10.
4 . 7 . 3 . Other parameters
To select the transducers and calibrate the measurement system, the
following are also determined:
• firing time: t = web to be burned divided by average burning rate;
• expected thrust: F = C F p 0 A t , where C F is the thrust coefficient of the
nozzle (approximately 1.5 for p 0 = 7 MPa).
104
Jean-Paul Bac
4.8. ANALYSIS OF THE RESULTING DATA
Figure 5 shows the definition of the parameters which need to be calculated
to do a thorough analysis of the firing test, based on the measurements
recorded (pressure or thrust versus time).
(1) Total combustion time, t cl
Determination of p min = atmospheric pressure + 1% of the maximum
capacity of the pressure cell, gives t x and t 2 ; and the t ci = t 2 — t x
(2) Effective combustion time, t ce and effective pressure, p e
Based on the curve p = f(t) obtained, these two parameters are calculated
through a series of iterations. They are related through the equation:
(3) Discharge coefficient, C D
Weight of propellant burned
= jr 2
pdt-A i m
•hi
(4) Average area of the nozzle throat, A (m
Because the variation as a function of time the throat diameter is not
available, it is necessary to calculate the average area of the throat, based an
mathematical averaging of the diameter before and after the firing.
(5) Mass of propellant burned
The propellant grains used must be carefully weighed during their manu-
facture.
Usually, the weight of the propellant grain is determined by deducting the
weight of the inhibitor from the total weight of the manufactured free-
Prediction and Measurement of Specific Impulse
105
standing grain. It may, however, be necessary to weigh the inhibitor
remaining after firing, particularly in the case of heavy ablation. If it is
necessary to take into account the weight of inhibitor burned, its contribution
is approximated as half of its weight in propellant.
(6) Average specific impulse , I sm
The average specific impulse of the rocket motor tested is calculated using
the equation
f 2 F dt
j — Jii
sm 9o x weight of propellant discharged
(7) Standard specific impulse , I sm
The average specific impulse corresponds to average operating conditions
that may deviate slightly from the targeted theoretical values (pressure,
expansion ratio).
Based on the values actually obtained during a test (e, effective pressure,
and atmospheric pressure), corrections are necessary to adjust the average
specific impulse to the standard conditions.
To achieve this, we rely on the fact that, with the same propellant grain and
similar operational conditions, the specific impulse of a rocket motor is
proportional to C F . This equation takes into account the data presented in
Chapter 1 which demonstrated the following:
• the existence of the equation: I s = C F /g 0 C D ;
• the assumption of the independence of the mass flow rate coefficient C D
from the combustion chamber pressure during firings with a pressure
close to standard conditions (7 MPa);
• The dependency of the thrust coefficient, C F , on the operating pressure,
the ambient pressure, and the cross-sectional area ratio (e) of the nozzle.
The standard specific impulse is calculated from the equation:
C F (calculated for standard conditions)
sm sm ^ (calculated for the exact operating conditions)
The values obtained range from approximately 170 s to 255 s, according to
the propellant families used.
Remark: In some cases the operating point of a rocket motor may not be
close to the standard conditions (7 MPa). In addition to the above correction
it is necessary to include the deviation of the mass flow rate coefficient as a
function of pressure. This deviation is calculated using and T 0 (Chapter 1).
The equation is written:
C F (standard conditions) * C D (operating point)
j s = J
sm sm ^ (operating point) • C D (standard conditions)
106
Jean-Paul Bac
4.9. ACCURACY OF THE MEASUREMENTS
Many parameters play a role in the quality of the measurement of the
specific impulse; they include:
• the accuracy of the pressure and thrust measurements (linked to the firing
bench, the sensors, and the measurement system);
• the precision of the calculations done from the firing measurements
taken;
• the accuracy of the evaluation of the weight of the propellant discharged
(involving the inhibitor, deposits inside the combustion chamber and on
the nozzle, and presence of unburned propellant in the inhibitor);
• insufficient knowledge of the variations of the throat area (and possibly of
the nozzle exit area) during firing;
• a mismatched nozzle, due to pressure variations in the combustion
chamber during firing;
• the presence of transitory phases (ignition phase and burnout phase).
As a result it is necessary to perform several firings under identical conditions
so that the evaluation of the specific impulse of a propellant grain may be
sufficiently precise (standard deviation o % 0.5-1 s).
5. Solid Fuels for Air-breathing Systems
5.1. THE PHYSICAL PHENOMENA
Missiles powered by solid fuel ramjets or ducted rockets use oxygen-
deficient propellants. The theory of operation has already been introduced in
Chapter 1. These propellants, which are further described in more detail in
Chapter 12, are greatly “under-oxidized”, i.e. they contain just enough
oxygen for complete gasification. These gases are formed in a primary
chamber from which exhaust flow is generally restricted by a nozzle or valve.
These gases flow into a secondary chamber, which is the real combustion
chamber of the ramjet. Another system, which as already been flight-tested on
a missile, did away with the intermediate nozzle by using propellants that
burn at the pressure of the ramjet chamber. This type of configuration is
called integrated gas generator or unchoked gas generator. For the two-
chamber system the fuel-rich gases are injected into the secondary chamber
where they mix with air coming through the air inlets located at the front of
the missile. The major technical difficulty is the adjustment of the combustion
gas flow rate to that of the air, to obtain a homogeneous and inflammable
mixture under the actual conditions in the secondary chamber. The theoreti-
cal problem is therefore mostly one of dynamics of fluids and chemical
kinetics. Thermodynamics helps to determine the upper value for the specific
impulse that can be obtained at the exit of the secondary chamber.
Prediction and Measurement of Specific Impulse
107
5.2. ORGANIZATION OF THE CALCULATIONS
5.2 . 1 . Determination of the properties of the
propellant in the primary chamber
This first calculation (following the model described in Section 2 of this
chapter) may be performed to obtain data for the thermodynamic parameters
and the composition of the combustion gases.
In reality the global performance of the system is more useful. Conse-
quently, the conditions in the secondary chamber are usually determined
directly.
5.2.2. Determination of the propellant gas/ air
mixture in secondary chamber conditions
This calculation is based on the conservation assumption of the total
dynamic enthalpy.
The calculation is the same as for a classic propellant grain. The only
difference is that the enthalpy in this conservation equation (h = h 0 ) is no
longer the propellant’s enthalpy alone, but rather the sum of the propellant
enthalpy and of the dynamic enthalpy of the air. We should note that the
static enthalpy of the propellant has already been actually transformed into
the combustion gas dynamic enthalpy, although it makes no difference for
this global assessment.
The zero-velocity assumption in the combustion chamber results in even
greater deviations than with classic rocket motors. In addition, since the
entropy of the mixing of propellant gas and air is not taken into account, the
total entropy gain in the chamber is higher than in a classic rocket motor, and
the efficiency is overestimated.
However, in spite of this, the value obtained through calculations is very
close to the values obtained through experiments.
5.2.3. Calculation of the expansion in the nozzle
This calculation is exactly the same as for a classic propellant grain, and
the approximations call for just about the same remarks.
The zero- velocity assumption at the nozzle entrance is even more difficult
to control. The additional amount of deviation is very small, however,
because the assumption of sonic speed at the throat of the nozzle remains
valid.
108 Jean-Paul Bac
5.3. PERFORMING THE CALCULATION
5.3.1 . Data entry
In standard calculations the data entry consists of the basic composition
and the enthalpy of formation of the propellant. In the case of semi-
propellant grains the proportions of the mixture, the propellant enthalpy, and
the dynamic enthalpy of the air are also needed.
All quantities are expressed in mass, whereby:
/ s is the stoichiometric ratio of propellant combustion gases versus air,
/ is the ratio of propellant gases versus air of the mixture analyzed
/
cp = - is called the equivalence ratio.
J s
The proportions of the mixture may be determined with:
• either the air and propellant gas flow rates;
• or the equivalence ratio <p of the mixture.
The dynamic enthalpy of the air is calculated with the assistance of a second
computer program based on the altitude and the Mach number. This same
program is also useful for the calculation of static enthalpy at any tempera-
ture and altitude. As a rule the calculations are limited to sea-level altitude,
which is a good representation for bench firing.
5.3.2. Results
With the propellant composition and the oxidizing potential, the values of
the thermodynamic parameters in the secondary chamber, at the throat, and
at the exit plane of the nozzle are obtained. For the various levels of cp
selected we therefore obtain the global specific impulse of the mixture which
can be expressed as:
• either the fuel-specific impulse (written: 7 S );
• or the air-specific impulse (written: 7 sa =/• 7 S )
The quantity /* 7 S is also known as the air-specific thrust.
In a diagram “7 s *p — /*7 S ”, where p is the density of the propellant, the
curve plotted for the various equivalence ratios characteristic of that particu-
lar propellant.
A comparison is generally made for the performance of the various solid
fuels, for the standard conditions (20°C, Mach 2, sea level), and recording the
values of 7 S • p obtained for an identical value of /• 7 S = 50 s.
The analysis of this diagram provides the values of corresponding / • 7 S for
a set performance level (7 S ). Because these values are directly tied to the air
Prediction and Measurement of Specific Impulse 109
consumption (/•/„ = 7 sa ), the selection of a solid fuel is possible by taking
into account the effect it will have on the size of the air inlets of the ramjet
(which can be a more or less important factor of drag).
Based on the solid fuel formulation, the specific impulse 7 S ranges from
approximately 600 to 1300 s. (For comparison purposes only, the specific
impulse 7 S of the solid fuel alone, calculated under standard expansion
conditions (7/0.1), is in the vicinity of 190 s.)
5.4. METHOD OF MEASUREMENT
Measuring the specific impulse of solid fuels for operating conditions of a
ramjet is vastly more difficult to do than measuring standard specific impulse
of a solid propellant. It requires testing installations which best simulate the
overall operation of these motors, and in particular, access to an air-supply
system.
Two types of test facilities are used, determined by the goal of the test
performed [8].
The direct connect setup: the air inlets of the combustion chamber are
directly connected to a hot air supply with a controlled flow rate. Because the
pre-heating of the air enables the enthalpy to be brought to the dynamic level
intended by simulation, this system offers a good representation of the
operating conditions in the combustion chamber. Since it is relatively easy to
set up, it is widely used. Unfortunately, because of its design it provides no
information whatsoever on the aerodynamic phenomena related to air inlets.
It is, however, the only system that allows easy thrust measurement during
the performance of the test.
In the free steam setup, the supersonic flow of air necessary to properly
simulate the actual supply of air to the air inlets is obtained by putting each of
the air inlets within the exit plane of a nozzle. These nozzles are fed by a wind-
tunnel system. In addition to the operating conditions in the combustion
chamber, this setup has the advantage of providing data on the aerodynamic
phenomena (shapes of the shock waves) linked to the actual geometry of the
air inlets. It also allows observation of the transition phase between the
burnout of the booster propellant grain and the ignition of the sustainer
propellant grain when dealing with a ramjet with integral boosters inside the
combustion chamber. This setup is much more complex than the previous
one, and requires the installation of powerful wind tunnels.
Bibliography
1. Gordon, S, and McBride, B. J., Computer Program for Calculation of Complex Chemical
Equilibrium Compositions , Rocket Performance , etc. NASA Lewis, SP, 273. 1971.
2. Zeleznik, J. K. and Gordon, S, Calculation of Complex Equilibria. Ind. Eng. Chem., 60(6),
27-57, 1968.
110
Jean-Paul Bac
3. Kinetics and Thermodynamics in High Temperatures Gases. A conference held at Lewis
Research Center, Cleveland, Ohio. NASA SP-239, March 1970.
4. Stull, D. R. and Prophet, H., Project Directors. JANNAF Thermochemical Tables . 2nd
edition. NSRDS-NRS 37. Catalog Number C 13. 48:37. US Government Printing Office,
Washington, DC, 1971.
5. Chase, M. W. et al , JANNAF Thermochemical Tables'. 1974 supplement, J. Phys . Chem . Ref.
Data 3, 311. 1974; 1975 supplement, J. Phys. Chem. Ref Data 4, 1, 1975; 1978 supplement, J.
Phys. Chem. Ref Data 7, 793; 1978; 1982 supplement, J. Phys. Chem. Ref Data 11, 3, 1982.
6. Banon, S. and Astier, J., The contribution of inert material to end burning propellant grain
performances. AIAA 86.1421; AIAA/SAI/ASME; 22nd Joint Propulsion Conference. 1986.
7. Collins, R. G., The AFRPL Ballistic Test and Evaluation System (BATES Program).
AFRPL Report No. TR-65-7. Air Force Rocket Propulsion Laboratory, Edwards, May 1965.
8. Mahoney, J. J., Salient characteristics and development status of ramjets for guided missiles
with emphasis on air launched tactical configurations. Naval weapons center technical memo,
TM4452, October. 1981.
CHAPTER 4
Solid Propellant Combustion
and Internal Ballistics of
Motors
BERNADETTE GOSSANT*
1. Introduction
The understanding and complete control of combustion are critical areas
of research when seeking better performance for solid propellant rocket
motors. The purpose of this chapter is to present the current knowledge in
internal ballistics of solid propellant rocket motors. Its first part deals with
the description of experimental determinations of the burning rate, necessary
for any internal ballistics calculations. A description of the combustion of the
various propellant ingredients follows. The last two sections of this chapter
are devoted to the combustion analysis under actual steady-state or unsteady
operation conditions of the rocket motor.
2. Solid Propellant Combustion
2.1. BURNING RATE
2. 7. 1. Background
The combustion of a solid propellant is characterized by the way its surface
regresses once it has begun to burn. The burning rate is the distance traveled
by the flame front per unit of time, measured normally to the burning surface.
This front is assumed to be regular and, in most cases, progresses in a
direction normal to itself. This has been experimentally verified (within the
*With the participation of Paul Tchepidjian.
Ill
112
Bernadette Gossant
precision limit of burnt profile measurements) by interrupting the propellant
combustion and examining the surface.
The burning rate versus pressure law is usually expressed by the formula
given by Saint Robert and Vieille:
r = ap n (1)
where:
n is the pressure exponent;
a is the rate of burning constant.
For a given propellant and a pressure ranging from 3 to 15 MPa, the pressure
exponent takes a typical value between 0.2 and 0.7. Some propellants,
however, have a different behavior: their pressure exponent is zero (the so-
called plateau effect), or even negative (mesa effect). The coefficient a in eqn
(1) is known to be dependent on the initial or in-depth temperature of the
propellant. An established empirical law is:
a = a 0 expO p (7i - Tf)] (2)
where:
Tf = an initial reference temperature;
Ti = the initial propellant temperature;
a 0 = the burning rate constant at Tf ;
a = the burning rate constant at T { \
Sensitivity of the burning rate at initial
temperature under constant pressure. As a first
approximation this coefficient may be considered as a
constant.
Finally, under certain extreme conditions (violent shock, explosion), the
burning rate may considerably increase and become greater than the speed of
sound. This catastrophic condition is called a detonation and is not discussed
in this chapter.
Tailoring a propellant will always include as major objective to minimize
the values of pressure exponent and temperature coefficient (Chapter 1),
while ensuring that its mechanical properties will still be sufficient for future
applications. There are a large number of physicochemical parameters
affecting the burning rate. They will be analyzed in detail when combustion
mechanisms of the main propellant families are described.
2. 1.2 . Experimental determination of the burning
rate
Several methods are used. Some of these methods require very small
amounts of propellant, and are therefore preferred when performing preli-
Solid Propellant Combustion and Internal Ballistics of Motors 113
minary analyses. The values obtained must later be confirmed at larger scale
(control propellant grains).
2. 1.2. 1. The strand burner method
In this method a small sample (standard size) of propellant is fired in a
bomb at constant pressure. This method has many advantages, including low
cost and quick-and-easy implementation. A disadvantage is that the reduced
size of the propellant sample may exaggerate the dependence on propellant
inhomogeneities.
(a) Preparation of the samples
The samples used are strands, with a square section (10 x 10 or 5 x
5 mm 2 ) approximately 170 mm long. They are inhibited along their whole
length to ensure that combustion occurs perpendicular to the surface. The
type of inhibitor depends on the propellant composition. Each strand is
perforated with four holes:
• the first hole, close to one end, is used to place the ignition wire;
• the other three, placed at 20, 85 and 150 mm respectively, are used to
introduce lead wires which, by melting, allow the electrical detection of
location of the flame front with time.
The samples are then placed vertically in a closed vessel, called a firing bomb.
(b) The firing bomb
The firing bomb currently used is made of steel (Fig. 1); its useful volume is
750 cm 3 . A preliminary pressurization is done, usually with nitrogen; the test
pressure level is kept constant during the combustion of the strand. Firings at
various temperatures are made possible with the use of glycol or oil baths (for
respectively low and high temperatures).
(c) Determination of the burning rate
The burning rate is obtained by knowing the burning distance as well as
the burning time between two lead wires. These lead wires, acting as fuses,
trigger a chronometer. As there are two strands per sample holder, four
determinations of burning rate are done per test.
2. 1.2.2. Liquid strand burner method [1]
This method also uses propellant strands. The strands, however, are
shorter (68 mm) and are only equipped with an ignition wire. The firing
114
Bernadette Gossant
Connecting head
with electrical wiring Locking ring
bomb is filled with water to ensure lateral restriction of the strand. It is then
pressurized to a desired pressure level, using nitrogen. This level, however, is
not regulated during firing.
The burning rate is obtained by knowing the strand useful length and the
duration of the firing. The latter is determined by monitoring the noise made
by combustion. The advantage of this method is that a preliminary lateral
restriction of the strand is not necessary.
2. 1 .2.3. Ultrasonic method [2]
(a) Principle of the method
A mechanical wave is produced by an ultrasonic transducer which works
either as transmitter or receiver. The ultrasonic wave travels through the
propellant sample and is reflected on the burning surface. Because there is a
tremendous difference in acoustic impedance between the propellant grain
and its burning products, it is possible to deduce the unburnt propellant
thickness by measuring the elapsed time between transmission and reception
of the wave. To avoid wave attenuation, the maximum propellant grain
thickness is 40 mm; the wave travel time is on the order of a few tens of
Solid Propellant Combustion and Internal Ballistics of Motors 115
microseconds. Changes in the thickness can therefore be monitored by
transmitting periodic ultrasonic pulses during firing. Instantaneous values of
the steady-state burning rate are obtained by derivation once the recorded
signals have been decoded.
(b) Test firing rocket motor
This experimental device consists of a small rocket motor in which a
cylindrical, “end-burning” sample of propellant (86 mm in diameter) is
mounted. For technical reasons (measurements of small thicknesses, thermal
insulation), a material with a similar acoustic impedance, called coupling
material, is placed between the receiver (transmission frequency 5-25 MHz)
and the propellant grain.
(c) Advantage of the method
This method allows the performance of direct, localized, and instantaneous
measurements. Only a small amount of material is used, and a large portion
of the burning rate law is obtained from just one firing. The pressure
evolution inside the combustion chamber is obtained either through the
geometry of the propellant grain, or by using eroding throats. However, the
coupling material needs to be tailored to each family of propellant.
2. 1.2.4. Standard ballistics test motors
These motors, used to verify the burning rate laws of the various propellant
families, are characterized by a low evolution of the grain burning surface. As
a result the firing may be done at practically constant pressure, which greatly
simplifies results analysis.
Star-shaped or slotted tube propellant grains, used to measure the specific
impulse, are discussed in their corresponding implementation in Chapter 3.
Some propellant compositions require burning rate measurements to be done
through end-burning grains (“cigarette-burning” combustion type). Table 1
provides an overview of the main characteristics of the various SNPE test
motors.
The effective burning time f ce is calculated from the pressure-time plot
(Chapter 3). Similarly, the same iterative procedure is applied to the burning
surface evolution curve versus the burnt propellant thickness; it gives:
• The “effective” surface area S e ;
• The “effective” burned web e h , such as:
S(e) • de = S e • e b
where e f is the propellant web thickness.
116
Bernadette Gossant
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Solid Propellant Combustion and Internal Ballistics of Motors
117
The calculation of the average burning rate is deduced:
2.2. COMBUSTION MECHANISMS
Except for the ignition phase, the combustion of a solid propellant is a self-
sustained phenomenon. Due to the heat feedback from the flame, the
temperature rise of the propellant located very close to the surface causes its
decomposition (structure changes, rupture of chemical bonds). Gaseous and
reactive chemical products are released, in turn feeding the combustion in the
flame zone.
2.2. 1. Description of the burning zone
Study of the burning zone takes into account, in addition to the flame zone,
the thin propellant layer close to the surface area where the temperature is
raised. Propellant is a poor heat conductor, and since the flame is very close
to the surface, the zone affected by combustion is very small. It is a few
hundreds of microns thick.
2.2. 7. 7. Description of the phenomenon in the solid material
With a uniaxial assumption, the integration of the steady-state heat
equation, including the following boundary conditions:
x = 0
T=T S
dr
X = — 00
T = Tj,
dx~°
gives the evolution of the temperature gradient in the steady-state regime
(origin of the axis on the burning surface as it moves). It is expressed by the
equation:
T=T i + (T s - T^cxpf-x)
( 3 )
where:
r = burning rate of the propellant;
T { = initial temperature of the propellant, far from the burning surface;
T s = surface temperature of propellant;
d p = propellant heat diffusivity.
118 Bernadette Gossant
(a) Decomposition in the solid phase
The following analysis does not take into account the chemical reactions,
thermally enhanced, occurring inside the propellant; those are endothermic
(decomposition of polymer chains) or exothermic (recombination in the
condensed phase of the chemical products resulting from the decomposition).
But temperature profiles recorded with very fine thermocouples on homoge-
neous propellant samples [3] reasonably validate eqn (3). Lengelle et al [4]
demonstrated that decomposition reactions practically occur only at the
surface.
(b) Kinetics of propellant grain decomposition: pyrolysis laws
• Composite propellants
Experience demonstrates that, for the steady-state regime, the regressive
burning rate r { of each ingredient is related to the surface temperature:
where:
( 4 )
A x = constant;
E { — activation energy decomposition reactions;
T s j — surface temperature;
R — universal gas constant;
i = stands for each propellant ingredient.
• Homogeneous propellants:
The integration of the conservation equation for the non-decomposed
propellant mass, assuming a zero-order reaction, gives:
where:
B x exp
dx
B p = constant;
£ p = activation energy of the propellant decomposition
reactions.
Taking into account the small thickness where reactions occur, Len-
gelle [5] shows that:
a
bj
1
fVp|"
to
w
73
V 2 RTj
IV L
T
1 s
2c P r Jj
( 15 )
Solid Propellant Combustion and Internal Ballistics of Motors 119
where:
d p = propellant thermal diffusivity;
T i = initial temperature;
T s = surface temperature;
g s = heat released by reactions in the solid phase
(breakdown of the N-N0 2 chemical bonds and the
reaction N0 2 + aldehyde in the condensed phase);
c p = propellant specific heat.
Experiments validate this relationship for this kind of propellant [4].
2.2. 1.2. Description of the phenomenon in the gas
Simplified, we may consider that the flame provides sufficient heat flux to
maintain the regression of the solid propellant surface through the gaseous
layer where the products released by reaction decompositions are hot,
although still inactive. In a one-dimensional assumption, resolving the heat
equation and assuming boundary conditions:
X
II
o
+
T = T S
, d T
X = x f
T = T { ,
dx
we obtain the following temperature profile:
T= T f + (T { — T s ) exp
exp
Krl/r ™ c g*f «
- / exp ~J 1 (6)
where:
T s = propellant surface temperature;
T { = adiabatic temperature of the flame;
x f = flame height;
m = mass flow rate of the gaseous reactive products;
c g = specific heat of the gases, at constant pressure (assumed to be
constant);
= heat conductivity of the gases, assumed to be constant;
Q F = heat released by the flame.
The value of the flame heat flux (in x = x f ) allows the computation of the
surface temperature T s :
T
1 s
= T f -
m c g x f
exp
m Cg x f
^T
(7)
120
Bernadette Gossant
Flame system
Kuo [6] presented a synthesis of the knowledge in this field. We will limit
ourselves to pointing out that there are two major types of flames that must
be considered when studying the combustion of propellants: laminar pre-
mixed flames, and laminar diffusion flames.
(a) Laminar premixed flames
In this case the molecules of the reactants are intimately mixed together.
The flame height is completely controlled by the kinetics of chemical
reactions.
*f = *r - ^2 B ( eX P ( - ( 8 )
where:
3 — order of the chemical reaction;
x r = height of the reaction;
E { = activation energy of the reaction;
B { = pre-exponential factor of the reaction;
p = combustion pressure.
(b) Laminar diffusion flames
Fuel and oxidizer are this time initially separated. The flame height,
depending mainly on the diffusion of the products, needed before any
chemical reaction, consists of two terms:
Xf = x d + x r (9)
• x r is the reaction height of the flame due to the intervention of kinetics
after the products issued from decomposition have been mixed.
• x d is this part of the total height which depends on the diffusion; it is
estimated from Burke-Schumann analysis [7]. This analysis deals with
the case of a Bunsen burner with two separate jets. It is applied by
analogy to the case of the reactions between oxidizing products coming
from the decomposition of ammonium perchlorate and combustible
products coming from the decomposition of the binder. In this section we
mention the equation for short flames which allows correlation of
analysis and experience [8].
2.2. 1.3. Energetic balance at surface
Continuing to assume that the reactions in condensed phase occur at the
level of the burning surface, we have:
Solid Propellant Combustion and Internal Ballistics of Motors
121
where:
A g , /l p = respectively, heat conductivity of the gas and of the propellant;
m = mass flow rate resulting from combustion;
Q s = energy representing the total reactions at the surface; this value is
negative if the final result is exothermic.
Therefore, using tiny thermocouples to determine the heat gradients on each
side of the burning surface [3,9] this makes it possible to calculate the value
of Q t .
2.2.2 . Combustion mechanism of extruded
double-base propellants (EDB)
2.2.2. 1. The various zones of combustion
Several combustion zones are observed (Fig. 2):
Zone 1 This is the zone where the propellant is not affected by the
combustion, although its initial temperature T { rises until it reaches
the value beyond which the reactions in condensed phase are
activated.
Zone 2 The foam zone, because of its foamy aspect. This is the zone where
the decomposition processes of the solid phase occur in a very thin
layer (10 -2 to 10 -3 cm) at moderately high temperature (600 K).
Some endothermic transformations produce liquids and gases: they
result from the thermal decomposition of nitrocellulose and nitrog-
lycerine. Other reactions, on the other hand, are exothermic (reac-
tions between decomposition products of the various propellant
ingredients).
Zone 3 The fizz zone, because of the fizzing aspect of the combustion. This
is the zone where the primary flame lies, resulting from the reactions
between the nitrogen peroxide and aldehydes produced by the
decomposition of the propellant. The proportions of the gaseous
products depend on the propellant composition, and especially
when there are specific ingredients controlling burning rate, called
ballistic modifiers or burning rate catalysts. In this zone the
temperature gradient is high; the adiabatic temperature of the
primary flame is about 1300 K.
Zone 4 The dark zone, because of its color. In this zone the gaseous
products produced by the primary flame are mixing; they become
hotter because of the heat flux transmitted by zone 5.
Zone 5 The final flame zone. In this zone combustion is largely completed.
The gaseous products produced by the primary flame have reached
the concentration and temperature necessary for the chemical
122
Bernadette Gossant
End of
primary flame
no 2 —
Aldeh. —
NO 0.25
N 2 0.02
CO 0.42
C0 2 0.15
H 2 0 0.14
H 2 0.006
Hydroc. 0.03
Mass decomposition ratio of the products in the different flame regions
Fig. 4.2. Burning zones of double-base propellants.
Surface
No 2
0.33
Aldeh.
0.35
NO
0.08
n 2
...
CO
0.1
C0 2
0.07
H 2 0
0.03
h 2
0.001
End of
secondary flame
NO 2
...
Aldeh
. -
NO
...
n 2
0.15
CO
0.28
C0 2
0.38
H 2 0
0.19
h 2
0.004
reactions to occur (NO/CO, H 2 reactions). The adiabatic tempera-
ture of the flame is around 2600 K.
2.22.2. Burning rate law and formulation parameters
The burning rate versus pressure law, for these propellants, depends on:
• the flame system;
• the apparition of a carbon deposit on the propellant burning surface.
The first part of this section presents the main trends for reference propellants
(without ballistic modifiers). Because they are not interesting for practical use
(very high pressure exponents), a second part discusses the behavior of
propellants containing ballistics additives.
Solid Propellant Combustion and Internal Ballistics of Motors 123
(a) Effect of pressure
At a specified pressure the intrinsic burning rate of an EDB propellant
depends most of all on its composition (Chapter 9). There are:
• so-called “cold” propellants with a heat of explosion around 800 cal/g;
• “hot” propellants, more energetic (approximately 1300 cal/g) and having
greater burning rates.
The distance of the flames from the surface is influenced by the pressure:
• Up to approximately 10 MPa, combustion is governed by the primary
flame. The N0 2 /aldehyde reaction has an activation energy of approxi-
mately 5 kcal/mole, and is distributed over the entire thickness of the fizz
zone; in addition, its order of reaction, close to 1, should lead to an n
value close to 0.5. The measured temperature of the flame, however,
depends on the pressure [11], and is higher than the adiabatic tempera-
ture calculated for the N0 2 /aldehyde reactions alone. Lengelle et al [4]
suggest that additional reactions between nitrogen monoxide and the
surface carbon deposit be taken into account. This increase in primary
flame temperature as a function of pressure level explains the high values
of pressure exponents (around 0.75) that are observed with uncatalyzed
propellants.
• At pressures above 10 MPa, the final combustion flame approaches the
burning surface and, because of its tendency to merge with the primary
flame, its heat flux also participates to the propellant decomposition.
Because of its energy characteristics (order of reaction of 2), the pressure
exponent is closer to one in this range of pressure.
(b) Effect of the ballistics modifiers
The introduction during manufacture of ballistic catalysts in the propellant
compositions allows the regulation of the burning rate level and a significant
decrease in the values of the temperature coefficient and of the pressure
exponent. In the pressure range of rocket motors, exponent values close to
zero can thus be obtained, thereby “flattening” the burning-pressure curve.
The most common additives are:
• lead salts;
• copper salts, mixed with lead salts (copper components alone are not very
active).
Their effect, depending on their amount, spreads over a certain range of
pressures. They produce an increase in the burning rate of the propellant
without catalysts (super-rate) while at the same time allowing the plateau
effect. Addition of carbon black permits the displacement of the pressure
range where the super-rate occurs.
124 Bernadette Gossant
(c) Initial super-rate
This occurs primarily at low pressure (<15MPa). Experimental data
published by Lengelle and Kubota show that the temperature of the primary
flame is increased by the addition of burning rate modifiers. These appear to
strengthen the reactions with the carbon deposited on the surface; in this case
the deposits become thicker. It seems necessary, however, to invoke other
mechanisms to explain the very strong effects observed: in some cases the
thick carbon deposit seems to act as a flame-holder, bringing the final flame
significantly closer to the surface.
(d) Second super-rate
This appears at high pressure. The carbon deposit on the surface has been
eliminated. On the other hand, spots, probably lead monoxide, have been
observed at the surface after extinction of strand burner samples.
Little is still known about the mechanisms that cause these super-rates,
particularly at high pressure.
2.2 2.3. The models
It would not be feasible here to provide a detailed analysis of each model.
We limit ourselves to citing the major ones:
• models taking into account, in various manners, the primary flame:
Kubota et al. [11], Beckstead [12], King [13], and Cohen [14];
• simulations of the complete flame system: Ferreira et al. [15].
2.2.3 . Combustion mechanisms of heterogeneous
propellants (inert and active binder
propellants)
Heterogeneous propellants contain a mixture of ingredients; each of them,
when decomposing, releases gaseous products whose nature is either oxidiz-
ing or reducing. The initial mixture allows a complete combustion, based on
the availability of chemical equilibria (Chapter 3). Nitramine molecules and
energetic binders both contain combustible and oxidizing agents, ensuring a
complete and independent combustion. In the following section we first
briefly describe the behavior of each main ingredient when subjected to a
significant heat source. This leads to a better understanding of the mechan-
isms observed in propellants.
Solid Propellant Combustion and Internal Ballistics of Motors 125
2.2.3. 1. Decomposition of the main ingredients of
heterogeneous propellants
(a) Ammonium perchlorate (AP)
Differential scanning calorimetry [16] has shown:
• that solid AP experiences a change of phase that corresponds to a change
in the crystal network at 513 K;
• the existence of two exothermic decomposition reactions in the con-
densed phase at approximately 570 K and 700 K.
Its melting point is 833 K. Linear pyrolysis tests have been performed by
Coates and Guinet [10]. Results obtained by Seleznev et al [17], however,
who used an optical method to determine the burning surface temperature of
strands, also serve as a reference.
AP combustion is sustained by the heat produced by the reactions in the
condensed phase and the premixed flame which lies very close to the surface.
The reaction between ammonia and perchloric acid, produced by AP
decomposition (adiabatic flame temperature is 1205 K, order of reaction 2
and activation energy approximately 1 5 kcal/mole, as established by Guirao
and Williams [18]), occurs at the surface. This reaction provides oxidizing
species.
The pressure exponent is high (around 0.77 between 2 and 10 MPa) and
there is a pressure threshold below which the combustion is no longer
sustained. It corresponds to a surface temperature equal to the melting
temperature of this oxidizer.
(b) Cyclic nitramines RDX and HMX
Two cyclic nitramines are used in propellant chemistry. The melting of
these ingredients (approximately 477 K for RDX and 553 K for HMX) is a
complex phenomenon: it has been observed, for instance, that the large
particles liquefy easier than the small ones. Solid HMX comes in four
different polymorphic forms, of which form /? is the most common. The other
forms (a, y, d) are successively obtained during a slow temperature rise. It is
not known whether they exist under the rapid heating conditions occurring
during combustion.
Boggs [19] and Fifer [20] have both written an exhaustive description of
the results of decomposition studies of these nitramines. The decomposition
reactions in the condensed phase lead to the rupture of the C-N and N-N0 2
chemical bonds. Analysis of pyrolysis gases shows the presence of N 2 , N 2 0,
NO, C0 2 , CO, H 2 , HCHO, H 2 0, and HCN. According to Fifer, the reaction
controlling the combustion is the reaction between aldehyde and N0 2 , very
126
Bernadette Gossant
rapid at the temperature reached. The flame temperature, contrary to the AP
flame, is very high (3286 K for RDX and 3278 K for HMX).
The burning rate law for HMX was determined using monopropellant
crystals or pressed strands [21]. Sample observation after extinction shows
the presence of a melted layer on the surface during combustion, with a
thickness depending on the pressure.
(c) The binder
In this section we only describe the case of inert binders, because the
combustion mechanisms of energetic binders are identical to homogeneous
propellant ones.
An inert binder is a polymer where C-C or C-H chemical bonds prevail.
Under the effect of heat these bonds break down. This reaction may occur in
the solid or the liquid phase, depending on the nature of the polymer. This
heat-related degradation results in the appearance of hydrocarbons that are:
• polymerized at the surface in the form of a charcoal residue or “char”, in
some cases;
• gaseous, and, when placed in an oxidizing atmosphere, burn with
diffusion flames.
The binder pyrolysis law can also be evaluated by thermogravimetry.
(d) Aluminum
Its introduction in compositions containing ammonium perchlorate allows
a significant increase of their adiabatic combustion temperatures. This effect
is due to the additional reaction for the formation of metal oxide. Since the
melting temperature of aluminum is 933 K, the micron-size particles con-
tained in the propellant melt at the surface where the temperature is generally
higher, and they gather into aluminum droplets. A detailed description of the
combustion of aluminum has been done [10]. In order to facilitate the
comprehension of the models, we shall only state that:
• the liquid droplets leave the surface and are oxidized at a significant
distance from the surface;
• the alumina particles formed in the combustion chamber of the propel-
lant grain are very small (approximately a few microns) and liquid
(A1 2 0 3 melts at 2318 K); they agglomerate or burst before they solidify
inside the nozzle, which ensures the gas expansion;
• Aluminum combustion is usually fairly well completed inside the
chamber. Some configurations, however, may decrease its efficiency when
aluminum residence time in the combustion chamber is too short.
Solid Propellant Combustion and Internal Ballistics of Motors 127
2.2.3 2. Combustion mechanisms of inert binder propellants
The following solid particles are dispersed in the binder matrix:
• oxidizer particles with large particle size distribution (1-400 /xm);
• and possibly, aluminum particles.
The following occurs during combustion:
• In the gaseous phase: all of the combustion reactions resulting in the
appearance of a complex flame system (Fig. 3):
reactions involving AP;
• In the gaseous phase: all of the combustion reactions resulting in the
appearance of a complex flame system (Fig. 3):
— premixed AP flamelets, considered as monopropellant. AP adiabatic
temperature, at a realistic operation pressure in the range of 7 MPa,
is approximately 1230 K;
— diffusion flames between the oxidizing products resulting from AP
decomposition or from AP premixed flame and the hydrocarbons
produced by the binder; the adiabatic temperature of the final
diffusion flame, for a non-metallized propellant containing 80% AP,
is in the range of 2300 K.
Diffusion flames
Fig. 4.3. Flame structure of heterogeneous propellant with inert binder.
128 Bernadette Gossant
(a) Burning rate law and composition parameters
For these propellants the burning rate law is a function of:
• the pressure range;
• the AP size distribution.
— At very low pressure, the burning rate is low and the heated
thickness of propellant is large compared to the size of AP particles.
Because the gaseous reactants produced by the various ingredients
have had time to mix, combustion is controlled by chemical kinetics.
The influence of the AP particle size is weak and the pressure
exponent is high.
— At medium pressure (1-15 MPa), the thickness of heated propellant
is less than above, and the diffusion phenomena between the reactive
gaseous products become controlling phenomena. Premixed and
diffusion flames are simultaneously observed, and the pressure
exponent value is moderate (0.3-0.4). In this pressure range the
burning rate is closely tied to the AP particle size: the finer the
ammonium perchlorate, the greater the burning rate.
— At very high pressure (p > 15 MPa), a new regime appears, with a
higher pressure exponent (0.6-0.7). The current models do not
predict this. It could be explained by a modification of the AP
pyrolysis law at high pressure. We may also think that under the
effect of the increase of velocity of the exhaust gases coming out of
the surface, or caused by the high pressure level, the heat transfers
are increased, in turn increasing the flux transmitted to the propel-
lant.
(b) Influence of ballistics additives
The additives used contain metallic atoms. Their action results less from
chemical reactions than from modifications of the thermal properties of the
burning surface:
• Some additives cause the formation of a very thin residue on the surface.
They must be well dispersed inside the propellant to ensure the most
efficient effect. Liquid additives are, for this reason, vastly preferable
(particularly for small oxidizer particle sizes), which explains the good
results obtained with ferrocenic additives.
• Other additives induce an increase of heat transfers as the diffusion flame
stands closer to the burning surface. In this particular case, metallic
oxides with sufficiently large particle size are used as flame-holder.
Solid Propellant Combustion and Internal Ballistics of Motors
129
(c) The models
From the various existing models [22], we would like to point out that:
• The first model developed by Summerfield et al . , the GDF model
(granular diffusion flame), studies the combustion reaction of oxidizing
gaseous “pockets” in the gaseous flow of binder decomposition gases.
Assuming that the size of these pockets is equal to the size of the solid AP
particles, there are two burning regimes:
— a low-pressure, premixed flame regime,
— a high-pressure, diffusion flame regime.
The resulting law is usually verifiable, up to approximately 15 MPa:
1 a b
r = ~p + 7*
premixed regime diffusion regime
where a and b (linked to AP particle size) are constant.
• Hermance calculates the mass flow rates of the binder and of the oxidizer,
and introduces the notion of delayed ignition of the AP particles as well
as a binder/oxidizer reaction at the surface. He takes into account the
possibility of a “turbulent regime” caused by the heterogeneity of the
combustion at the propellant surface. This regime modifies the thermal
characteristics of the gases and causes an increase of the pressure
exponent when the flow rate is significant.
• The BDP Model (Beckstead et al. [8]) takes into account a complex and
more realistic flame system: a control parameter is used to adjust the
flame’s relative importance in accordance with the pressure range. At low
pressure the primary flame is prevalent (HC10 4 /hydrocarbon). At high
pressure it is replaced by the AP premixed flame and the final diffusion
flame (oxidizing products produced by the A P/hydrocarbon flame).
Binder and AP surface temperatures are assumed to be the same. A
statistical analysis using pyrolysis laws and taking into account the AP
size distribution, reputed to be unique, allows calculation of the binder
and AP mass flow rates.
• The PEM model (Petite Ensemble Model) offers the possibility of
performing a more detailed analysis of the heterogeneities of the surface,
coming from a better modeling of oxidizer particle size distribution. By
supposing that each flamelet is linked to a particle surrounded by a thin
binder coating, and that all these small flames do not interact among
themselves, the propellant can be regarded as a collection of simpler
propellants (one particle size log-normal distribution) called pseudo-
propellants. The description of the combustion of each pseudo-propellant
uses the same flame system as the BDP model. Its mass flow rate is
calculated on the basis of AP particle combustion as a function of time.
130
Bernadette Gossant
As in the case of BDP, mathematical formulae allow for evaluating
geometry of the pseudo-propellant burning area. The PEM model assigns
an identical value to the surface temperature for the binder and the
oxidizer of each pseudo-propellant. The burning rate of the entire
propellant is determined by averaging the burning rates of each pseudo-
propellant.
• In France, the method developed by ONERA [23] is similar to the last
two models. The flame system is the BDP system, with the exclusion of
the primary flame. The calculation of the mass flow rate is also done as a
function of the combustion time of a particle. But the pyrolysis of the
ingredients is determined by using two different surface temperature
values, one for AP and the other for the binder. Like the PEM model this
method allows computations for several different values of the filler
particle size.
22.3.3 . Combustion mechanisms of advanced energetic
binder propellants
RDX or HMX, which significantly increase the specific impulse, are
introduced in the EDB-type binder. These are the so-called composite
modified double-base propellants. They are divided into two families
(CMCDB and XLDB), based on their manufacturing process and resulting
different ballistics characteristics (Chapter 11). Because their combustion
mechanisms are very similar, the following section discusses only those
related to XLDB propellants. Their performance level may be further
increased by adding ammonium perchlorate and aluminum to their ingredi-
ents (NEPE propellants). The preceding discussion on the various ingredi-
ents behavior of homogeneous and heterogeneous propellants will now help
to understand better the combustion mechanisms of these two major families
of solid propellants.
(a) Combustion mechanisms of XLDB propellants
Observation of the burning area
By observing the combustion of samples, we see that nitramine particles
melt at the surface, under the effect of heat flux. Therefore an intimate
mixture, close to the surface, of the various gaseous species takes place,
facilitating reactions led by premixed flames. We know that the nitramine
molecule has a balanced amount of oxidizer and reducer. In addition, the
combustion products are mostly N 2 , CO, and H 2 0. Since the products of the
primary flame are mainly NO, CO, and H 2 , we may safely assume that there
is no interaction between the various flame systems.
Burning rate law and formulation parameters
The burning rate law of a polyester binder is shown in Fig. 4. It is close to
that of a “cold” extruded double-base propellant. We also see, in this figure,
Solid Propellant Combustion and Internal Ballistics of Motors 131
that it is slightly modified by the addition of nitramine. The propellant
burning rate realizes a compromise between the burning rate of the binder
and that of the nitramine. Experience has also shown that the size of the
particles has no effect on burning rate: this is explained, at least at low
pressure, by the nitramine melt layer at the surface. Finally, we see that the
exponent remains very high, regardless of the pressure level.
Influence of the ballistic catalysts
Fifer [20] has summarized the main results already known concerning the
catalysis of these propellants. When researching ballistic catalysts it is
necessary to act either on binder or on nitramine.
• Catalysts of binder decomposition
Catalysts used with homogeneous propellants (lead salts) develop a
carbonized layer at the surface, leading to a strengthening of the NO-C
reactions. They cannot, however, all be used with a polyester binder,
because they catalyze the cross-linking reaction, resulting in an unaccept-
able rise of propellant viscosity during processing. Some of these catalysts
induce super-rates, although less spectacular than with homogeneous
propellants: the thickness of the carbon deposit at the surface is, in this
case, certainly less than with nitroglycerine- and nitrocellulose-based
propellants.
p(MPa)
Fig. 4.4. Burning rate laws for propellant and basic ingredients.
132 Bernadette Gossant
• Additives facilitating nitramine decomposition
Because of the large quantities of nitramines added to the propellant,
another possibility consists in facilitating the decomposition of the filler.
Today, part of the research efforts are oriented to the development of
products that would have such effects.
(b) Combustion mechanism of NEPE propellants
Observation of the burning area
Current compositions use a polyether binder, more heavily oxygenized
than a polyester binder. In addition to the nitrated plastifier and the
nitramines already contained in the XLDB propellants, NEPE propellant
performance is increased by adding ammonium perchlorate and aluminum.
By introducing ammonium perchlorate, the structure of the flame zone is
significantly modified. Oxidizing species resulting from AP decomposition
and hydrocarbons produced by the binder form diffusion flames leading to
the disappearance of the very characteristic dark zone. The flame of a NEPE
propellant is very much like the flame of a heterogeneous inert binder
propellant.
Burning rate law and composition parameters
• Behavior of the binder
Although the burning rate laws of polyether and polyester binders are
very close, when ammonium perchlorate is added the polyether binders
show very peculiar behavior. Experience has shown that it is capable of
dissolving a non-negligible quantity of AP; saturation was seen at a 6%
mass ratio value of AP/(AP + binder). The portion of dissolved AP
brings about the appearance of a premixed flame with the gaseous
products of the binder. The burning rate of the so- “filled” binder
increases rapidly and its pressure exponent is high.
• Propellant burning rate law
Due to the formation of diffusion flames, the propellant burning rate
depends on the AP particle size. While keeping constant AP content in a
formulation, the burning rate can be improved by using micron-size
particles. The addition of increasing quantities of AP promotes the
formation of diffusion flames, particularly in the cases of medium or large
particle sizes; lowering of pressure exponent is subsequently observed.
3. Steady-State Combustion in a Solid Propellant
Rocket Motor
The causes of the modification of propellant burning rate law are studied in
this section which also deals with methods used to predict the steady-state
operation of a rocket motor.
Solid Propellant Combustion and Internal Ballistics of Motors 133
3.1. MODIFICATIONS OF THE BURNING RATE LAW
INDEPENDENT OF THE INTERNAL AERODYNAMIC FIELD
3 . 1 . 7 . Modifications caused by involved materials
3. 1. 1. 1. Modifications occurring at the propellant/ insulator
interface
In the case of an end-burning combustion mode, the solid propellant grain
is particularly susceptible to this phenomenon. An analysis of the burning
front after quenching often shows a surface deformation, easily explained by a
modification of the burning rate in the immediate vicinity of the thermal
insulator (Fig. 5).
Pressure/Time Curves and Corresponding
Surface Profiles
Super-rate along the insulator
Fig. 4.5. Visualization of the regression front of an end-burning grain.
134
Bernadette Gossant
(a) Origin of local burning rate modification
• Large concentration of fine particles in the area close to the inhibitor, or
peculiar distribution of the particles in that area
These particles may be ammonium perchlorate, anti-instability addi-
tives, or ballistics catalysts used in solid form. If finely divided, all these
ingredients increase the burning rate values. Messner [24] indicates that
super-rate values of 70% have been obtained with compositions contain-
ing iron oxide. Smith [25] comments on tests demonstrating the accumu-
lation of AP close to an interface. Jolley et al. [26], however, believe that
this behavior does not systematically occur.
• Migration of propellant liquid ingredients at the interface
During curing, when the propellant is still a dough, and to a lesser
degree during aging, the migration of the plasticizer and/or of the ballistic
additive may occur. Any displacement of the plasticizer in the inhibitor
leads to a local increase in the propellant filler content as well as to a
growth in the burning rate. Conversely, a local thinning in ballistic
additives content of the propellant decreases the burning rate, but the
progression of the flame front in parallel layers tends to counteract this
effect.
• Conduction heating of the material near the interface
This phenomenon, resulting from the heat transfer to the motor walls
caused by gas flow inside the combustion chamber, occurs consecutively
to the temperature rise of the propellant in immediate contact with the
heated materials. This situation is more likely to happen during the firing
of solid free-standing end-burning grains. The flow of heated gases in the
gap between the case and the grain may induce local heating of the
insulator and of the propellant in contact.
(b) Remedial measures
• In the case of active binder propellant grains
Here we are concerned with the absorption of nitroglycerine by the
thermal insulator: the propellant heat of explosion locally decreases, but
the percentage of ballistic additives is clearly increased. The use of highly
cross-linked inhibitors or silicones is recommended. A primer (poly-
isocyanate) may also be interposed, which, delaying ingredients migra-
tion, provides the insulator with sufficient time to acquire mechanical
strength. When thermal heating of materials occurs near an interface, the
addition of an ingredient with endothermic decomposition may prove
useful to limit the super-rate.
• In the case of inert binder heterogeneous propellant grains
The super-rate decreases by slowing down migration of the plasticizer
Solid Propellant Combustion and Internal Ballistics of Motors
135
in the bonding resin, usually of a polyurethane type. This can be done by
using high cross-linked polyurethanes or primers acting as barriers
against migrating species.
3. 1 . 1.2. Controlling the burning rate
(a) Technology used
There have been a large number of studies to evaluate the advantage of
end-burning propellant grains with locally controlled burning rates. Two
techniques were examined.
• The first technique consists in incorporating strands of propellant
perpendicular to the surface, these strands having a higher burning rate
than the matrix propellant. No heat exchange occurs between the two
propellants because they are good heat insulators, and the angle of
resulting cones in the slower composition depends on the ratio between
burning rates at the specified operating pressure [27];
• With the other technology, the super-rate effect is obtained by incorpor-
ating metal wires inside the propellant grain. These wires melt at a
relatively low temperature, conduct the heat very well, and transmit a
heat flux to the adjacent propellant, raising its initial temperature and
therefore its local burning rate. The wires used are typically made of
copper or silver. The design of these wired grains is discussed in Chapter
2 .
3. 1.2. The hump effect
3. 1 .2. 1. The phenomenon
The hump effect — also called BARF, BRAF, SBRE or RAINBOW when
used to indicate the effects due to mechanical stresses in composite propellant
grains — refers to an overpressure during firing that may reach 8% of the
planned value. This overpressure is not constant during operation. The
corresponding time depends on the propellant grain geometry. In a BATES
grain, for instance, it corresponds to the point where approximately half the
web is burned. This phenomenon may occur in many internal configurations:
it has also been observed on star-shaped grains.
The result analysis of such a firing is based on internal ballistics laws,
assuming that the burning rate law of the propellant is the same in any point
136
Bernadette Gossant
of the grain. This analysis then provides the evolution of the burning area,
becoming an equivalent area, as a function of the burnt thickness. When the
hump effect occurs during a firing, comparison of the previous analysis with
the theoretical curve of the evolution of the burning area clearly demon-
strates the presence of differences (Fig. 6). Those primarily depend on AP, its
ratio and size distribution in coarse and fine particles [27,28], and on the
presence of aluminum in the composition.
3. 1.2.2. Influence of processing
An analysis of results obtained after extinction of a BATES propellant
grain at the maximum value of overpressure, shows that hump effect is caused
by a burning rate law change as a function of the propellant thickness.
Friedlander and Jordan [28] offer the same interpretation. The explanation
may be a peculiar distribution of the propellant solid fillers, induced by the
manufacturing process.
3. 1.2.3. Taking the hump effect into consideration for
ballistics predictions
Currently, it is only through accumulating results analyses from firings
that an average and empirical law of burning rate deviations for a specific
propellant grain may be obtained, of the form:
r f =m
r o
Fig. 4.6. Comparison of burning area evolutions of a BATES grain.
Solid Propellant Combustion and Internal Ballistics of Motors
137
where:
r r is the actual burning rate of the propellant during firing;
r 0 is the known burning rate of the propellant, excluding the hump effect;
e is the burnt thickness.
As a rule, the ratio r r /r 0 varies by 5% in a range from 0.95 to 1.05. For some
grain shapes (tubular, star) with a mainly radial burning the above law
exhibits a hump when plotted. For more complex shapes (FINOCYL type)
with a combination of several types of combustion (in R , Z and 0 ), the curve
has the shape of a sinusoid.
Currently, precise ballistics predictions presuppose a sufficient number of
results from experiments the analysis of which helps estimating the r r /r 0 =
f(e) law which has to be considered in the computations.
3.1.3. Mechanical stresses
Mechanical stresses occur in case-bonded propellant grains:
• during the cooling period after propellant curing;
• during operation, when the combustion chamber is pressurized.
In some cases these stresses modify the burning rate law.
3. 1.3. 1. At the bonding interface
Kallmeyer et al [30] demonstrate the increase of the super-rate at the
propellant/inhibitor interface as a function of the bonding stress level; this
stress level is a function of the difference between curing and firing tempera-
tures.
3. 1.3.2. inside the propellant
Internal stresses cause dewetting to occur between the various fillers and
the binder; dewetting increases with load intensity. As a result the propellant
acquires a certain internal porosity and becomes compressible. An increase in
the burning rate is then observed [31]. Figure 7 illustrates this effect on a
strand which has been first strained, then inhibited with a stiff agent strong
enough to maintain elongation. The burning rate change does correspond to
the beginning of the strand volume variation.
3. 1.4. Acceleration
The motor operation, in flight, may be modified by the acceleration of the
rocket. This modification is particularly clear with aluminized propellant
grains.
138
Bernadette Gossant
Fig. 4.7. Influence of propellant elongation on the burning rate law. Burning rate
vector parallel to the tensile stress.
Extinguishments have shown that the burning surface of this type of
propellant, when submitted to a normal acceleration directed toward the
propellant, exhibits a large number of small conical craters. They are caused
by amounts of aluminum droplets which contribute to heat conduction at the
surface and consequently significantly increase the burning rate at the point
of contact. When an aluminum droplet becomes larger (and probably
oxidizes), the burning rate at the bottom of the crater slows down (though
remaining greater than the burning rate without acceleration). The bottoms
of the craters flatten themselves out.
Based on studies done on this subject, and illustrated by Fig. 8, we note
that this type of phenomenon occurs when:
• the acceleration exceeds a threshold value which is a function of the size
of the aluminum particles and of the burning rate (approximately 10 g for
Fig. 4.8. Effect of acceleration on motor operation.
Solid Propellant Combustion and Internal Ballistics of Motors 139
propellant grain burning at 5 mm/s and containing aluminum particles
measuring 5 jam);
• the angle between the acceleration and the burning surface normally does
not exceed a threshold value (of about 20°); beyond that value, the
influence of acceleration on the burning rate is negligible.
3.2. DETERMINATION OF THE FLOW FIELD
3.2 . 1. Background and fundamentals
The simplified analysis [33] of the motor stationary operation is based on
the possibility of realizing equilibrium between:
• the mass flow rate produced by the burning surface of the propellant
grain;
• the mass flow rate the nozzle can eject.
The steady-state regime resulting when the two are matched, and related
specific fundamental equations, were discussed in Chapter 1. Continuing to
assume that combustion and expansion of burned gases form two separate
phenomena, respectively taking place in the combustion chamber and in the
nozzle, we are able to analyze the transient regime associated with grain
ignition and burn-out phases.
3. 2. 1.1 . Transient regime
While we disregard the volume variation of the central port resulting from
combustion (rather small since transient phases are short), we do include the
term representing internal gaseous mass variations, which stands for the
filling (or emptying) of the central port, and is tied to gas compressibility.
Therefore the exhaust mass flow rate coming out of the nozzle corresponds to
the mass flow rate emitted by the propellant burning surface less the build-up
term. The continuity equation is written:
where:
d Pc
5 d t
+ Pc —
m
C D A t
( 11 )
t s = V/(r T c C D A t ) = the residence time;
V = volume of the chamber;
p c , T c = pressure and temperature of the chamber;
140
Bernadette Gossant
A t = area of the nozzle throat;
m = mass flow rate of the propellant grain;
C D = propellant discharge coefficient;
r = R/M where R is the ideal gas constant, M is the gas molecular
weight.
(a) Pressurization
Assuming the validity, under these conditions, of the steady-state burning
rate law as well as instantaneous ignition of the entire surface of the
propellant grain, the pressure evolution is given by:
(1 -n)f-
l') !/l -n
( 12 )
where p c0 is the chamber pressure corresponding to stationary operation.
(b) Depressurization
Assuming a sudden extinction of the entire surface, we have:
Pc = Pco exp
(13)
3.2. 1.2. Requirements when designing a propellant grain
The steady-state regime assumption of Chapter 1 and the simplified
reasoning above turn out to be insufficient, for several reasons:
• It only gives an average value for the pressure. This pressure level is
uniform in the entire combustion chamber. Its evolution, as a function of
propellant thickness, is known as long as the operating point can
reasonably be approximated by a succession of discrete equilibria.
• The pressure variations inside the combustion chamber are not deter-
mined; they must be known to assess the structural integrity of the
propellant grain, particularly at the onset of the firing. They also must be
determined in conjunction with the local burning rate expressions (e.g.
eqn (1)).
• The gas velocity inside the combustion chamber being assumed to be
zero, risks connected with heat transfer increase, as well as erosive
burning, cannot be taken into consideration.
Solid Propellant Combustion and Internal Ballistics of Motors 141
• There is no modeling of the non-steady phenomena: eqns (12) and (13)
hold a limited validity for the transient sequences. In addition these
assumptions do not include variations of the propellant discharge
coefficient.
More complete models should include unsteady phenomena and are there-
fore necessary for a precise knowledge of the internal aerodynamics.
3.2.2 . Conservation equations in fluid mechanics
The fluid domain consists of the combustion chamber and nozzle. Some of
the boundaries are inert ones, i.e. inert parts of the combustion chamber and
of the nozzle. The burning surface, on the other hand, is an injecting
boundary which, over time, moves along its normal at a velocity r (propellant
burning rate law).
SNPE computer codes solve the fluid mechanics equations while respect-
ing the conservation conditions relative to the mass, momentum and energy,
within a framework of restrictive assumptions concerning the nature of the
fluid and its heat exchanges with the case walls:
• The fluid produced by the propellant combustion is a gas assumed to be
ideal and heated at a high temperature.
• The fluid is non-viscous, non-reacting and non-conductive. There is no
heat exchange with the walls. The boundary with the burning propellant
occurs at the end of the flame; the flame height is assumed to be
negligible.
• The fluid is single-phased. There is no need to introduce the condensed
phase because neither the pressure fields nor the burning rate are
basically modified by its presence. It should, however, be taken into
consideration in any realistic performance prediction (Chapter 3).
3.2.3. Solving the one-dimensional equations
3.2.3. 1. Local equations
Each term of the conservation equations will be assessed in the fluid sector
shown in Fig. 9. This sector has two stationary boundaries (A x and A 2 ) and a
moving boundary S.
142
Bernadette Gossant
Fig. 4.9. Element of fluid. One-dimensional assumption.
(a) Absolute velocity of the gases at the combustion wall
The fluid velocity at the wall is assumed to be the exhaust gas velocity
released at the wall. Here, the equation of mass conservation requires:
pv r = p p v
(14)
where:
p, p p = density of, respectively, the gases and the propellant;
v r = velocity of the gases relative to the wall;
v = absolute velocity of the wall
Therefore:
v r = v g -v (15)
where v g is the absolute velocity of the gases at the wall.
Taking into account the respective orientation of each of the vectors, we
find:
v
g
(16)
(b) Continuity
With:
u = flow velocity vector
n = vector perpendicular to the surface. The term of the exhaust flow is
calculated for A l9 A 2 , and S (the normal directed outside the field)
Solid Propellant Combustion and Internal Ballistics of Motors
from:
143
[m - t5] • n
[m — t>] • n
= u ■ n = — u(Zi )
A 2
= u-n = u(z 2 )
[u — t;] • n
= v - v-n = - (d + i>)
knowing that:
, „ _ _ dz dA v
d S = 2nR — — — - = 2nR
cos 0’ dt
and for a small dz increase, we have:
cos 0
(17)
(18)
(19)
( 20 )
(c) Momentum
Assuming a uniaxial flow along the z axis, the projection on z of the
tensorial product of the equation below must be calculated:
f pudV= — f p[u ® (u — £)]« dS — f ( pI + T)ndS
vtJVit) Js(t) JS(t)
where:
T = deviator of the tensor of the second order, representative of viscous
tensions;
/ = identity matrix;
HO = moving volume limited by the surface S(t)
We obtain:
Proj on z[u ® (u — u)]w
Proj on z[u ® (it — u)]h
Proj on z[u ® (u — v )]«
= [u ® u]n
= [u ® u]n
= - w 2 (zi)
^2
= u 2 (z 2 )
A 2
= - v (v + u)sin 9
( 21 )
( 22 )
(23)
144
Bernadette Gossant
Taking into account that dA/dz = 2nR tg 0, and by making z x approach z 2 ,
we obtain:
d d - dp jV-dA
- ft (p„A) + ^puA) + A rz -e,, - Tz
(24)
(d) Energy
When it is integrated over the volume F(t), the local conservation equation
for energy gives:
d_
Tt
P\ e + j )dF=
- L i e + 1
-I
(u — v)n d S
(p-« + T • «)n dS — [ q ridS
S(t) JS(t)
The various terms are assessed as above, and the local expression is
written:
k (p£A) + Tz (psuA) + T (puA) = ir[ pV 1 + p ’- £b ] (25)
where:
e = total internal energy of the gaseous discharge, e — u 2 / 2, where e
represents the internal energy of the fluid;
£ b = total internal energy of burned gases as they are created
= e b + v 2 /2, where e b represents the internal energy of the
burned gases.
3.2.3.2. Computer codes for calculations of one-dimensional
equations
There are several codes, because the one-dimensional assumption is fairly
well justified for propellant grains with a high “length versus diameter” ratio
and a gas flow section area that evolves slowly. This assumption allows rapid
executing times. We will limit ourselves to one example: PROCNE 1 [34],
which is very widely used for preliminary propellant grand design analyses.
The unsteady terms of the conservation equations are taken into account.
The fluid domain is shared into discrete sections along the axis of the
propellant grain: it includes the combustion chamber and the nozzle. The
Solid Propellant Combustion and Internal Ballistics of Motors 145
numerical procedure selected for this code is the fractional two-steps method,
proposed by Yanenko [35]. PROCNE 1 code is used to calculate the
evolution of the internal aerodynamic field while taking into account the
geometry evolution as a function of time. Figure 10 compares predicted
pressure and thrust levels to experimental results for a nozzleless motor.
3.2 .4. Calculation of conservation equations for
complex geometries
Improved ballistics performances of rocket motors are obtained through
propellant volumetric loading fraction enhancement, typically realized with
complex geometrical shapes. Such configurations entail the presence of
significant variations in the pressure and fluid velocity, as well as the
possibility of couplings between the propellant burning rate law and the local
Fig. 4.10. Comparison between prediction (PROCNE) and experiment (nozzleless
motor).
146
Bernadette Gossant
aerodynamic field. Consequently, the fluid mechanics equations must be
resolved in a situation which is as representative as possible.
3.2.4. 1. Fundamentals of the two- and three-dimensional
codes
The numerical scheme used to solve the governing equations was created
by Godunov et al [36]. A few reminders on shock waves and discontinuity
decomposition are necessary before discussing this procedure.
(a) Shock waves
First, some fluid mechanics notions: given a source S of small perturba-
tions in a motionless fluid or in a uniform motion (Fig. 11):
• Motionless fluid: u = 0
A perturbation occurring at time t = 0 propagates at the speed of sound a
in all directions and occupies at time t a spherical surface with a radius value
of at.
• Fluid in uniform translation, with u < a
In a subsonic flow the perturbation spheres are inside each other, and
surround the source. With sufficient time the perturbations reach every point
of the fluid.
• Fluid in uniform translation, with u > a
In a supersonic flow the perturbation waves occur within an envelope.
Only the areas within that envelope are affected by the perturbations.
• Formation of a discontinuity
a = Speed of sound
Fig. 4.11. Propagation of small perturbations in a uniform flow fluid.
Solid Propellant Combustion and Internal Ballistics of Motors 147
In a fluid activated by a slight compression the successive waves will
propagate faster and faster because of the rise in temperature of the medium,
finally catching up to each other and forming a compression wave. In the
opposite case, when the fluid is subjected to a slight expansion, the waves no
longer catch up with each other because of temperature decay: a discontinu-
ous expansion wave does not occur in most gases, although it may occur in
some computational methods.
• Evolution through a flat discontinuity surface (Fig. 12)
When going through a discontinuity surface a compressible fluid is
subjected to finite pressure and temperature variations, but its velocity
suddenly varies in magnitude as well as in direction. The conservation
equations on the ABCD volume are written as follows:
• Mass conservation
Pl U ln ~ P2 U 2n
Momentum conservation
Pl + P 1«1» = Pl + Pl »ln
where u lt = u 2t
Energy conservation assuming adiabaticity:
(26)
(27)
7 Pl U 2 n
y Pi
2 + y-lPi 2 + y-\p 2
= _l±L [ c i y- 1 ^] (29)
2(y — l ) L 7 + 1 U J (
where c —
A>' - 1) _
JTT c ' t -
Fig. 4.12. Flow field evolution through a discontinuity surface (I).
148 Bernadette Gossant
to which the equation of the ideal gas state is added:
Pi^Pi'Tu p 2 = p 2 rT 2
where r = R/M = specific gas constant
Hugoniot/relationship
This determines the relationship between p u p l5 p 2 and p 2
1
p2 y — i Pi
pi y + i Pi
7-1 Pi
This relation is definitely different from the isentropic:
Pi
El
Pi
Through a shock wave, the fluid therefore undergoes an irreversible
evolution. The entropy for an ideal gas is given by:
= c - ln (^)
+ constant
The Hugoniot relationship expresses an actual physical evolution only
when it corresponds to an increase of entropy.
(b) Process for discontinuities analysis
Godunov et al. [36] propose the following method: when two masses of the
same gas, assumed ideal and compressed at different pressure levels, come
into contact, the contact surface forms a discontinuity surface within the
initial pressure distribution. The physical values on each side of the surface
may undergo any sort of jump. Discontinuity, however, can exist as a stable
formation only if it satisfies certain conditions; if not, it breaks down into
several discontinuities becoming distant from each other with time. Conse-
quently, several configurations may occur. Pressure and velocity values on
each side of the contact discontinuity are identical; density and internal
energy differ, on the other hand. These two fields are themselves separated
from the non-perturbed area by either a shock wave or an expansion wave.
Solid Propellant Combustion and Internal Ballistics of Motors
149
Location
CD Contact Discontinuity p,P Local pressures
SW Shock wave u,U Local velocities
EW Expansion wave P,R Local densities
e,E Local energies
Fig. 4.13. Discontinuity splitting between two gaseous masses.
Figure 13 illustrates the one-dimensional case of a shock wave to the left and
an expansion wave to the right. These are usually expressed as follows:
• Left-hand wave:
• Right-hand wave:
U - u,
~ Pi
p
U - u
II
P ~ Pn
fin
= 0
For a shock wave
A =
Pi
( 31 )
( 32 )
( 33 )
where i = I or II, depending on whether the wave is to the left or to the right.
For an expansion wave:
p> =
2y
Pi «i
1 -
y-i/2y
( 34 )
150
Bernadette Gossant
where:
a { = the sonic speed of the medium i =
i = I or II, depending on whether the expansion wave is to the left or to the
right.
Consequently, the configuration appearing when two gaseous masses come
into contact can be determined. Elimination of U between eqns (31) and (32)
allows the determination of P solving:
F(P) = «, - Un = =f(P, p„ p.) +f(P, p,„ p n ) (35)
Pi Pii
with:
P-Pi
f(p, p,. pd =
}
i 1
y - 1
2
p\y-lf2y
where P > p t
where P < p t
(36)
The analysis of the function F(P) reveals several possibilities. Assuming
that p, < p„ and writing:
F(Pn) ^shock
Pn - Pi
V p ')
(37)
(38)
• If 0 < P < p I} two expansion waves propagate, one to the left and one to
the right. We have:
U l ~ M II ^ ^exp
• If pj < P < p n , a shock wave develops to the left and an expansion wave
develops to the right. In which case:
U exp < u, - u„ < (/ shock
• IfP > Pn, two shock waves propagate, one to the left and the other to the
right. In which case:
«I - “n ^ ^shock
The value of P is determined by resolving eqn (35), proceeding by
successive iterations using Newton’s tangent method which, as indicated by
Solid Propellant Combustion and Internal Ballistics of Motors 151
the authors, ensures a rapid convergence from an initial value. The other
parameters are calculated using the P value at convergence [36].
(c) Numerical procedure
Looking at the difference scheme for the unsteady one-dimensional
equations of the fluid dynamics developed by Godunov et al . , we are
provided with a simple illustration of the method. Assuming density p,
impulse pu, and total energy p(e + u 2 /2) constant on each elementary part of
the field, the conservation equation laws (described in section 3.2.2) although
simplified in terms of the fluid behavior and applied to grid j — 1/2 (part
XjJ) for the period of time from t to t + At, are written as follows:
(p j ~ 112 - Pj- 1 / 2 )(Xj - Xj _,) + A£([Kl/],. - [*[/],._,) = 0
([pu] J_1/2 - + At([P + RU 2 \ - [P + RU 2 ~\j-i) = o
-H £ + t) +
Indices in lower position stand for the values at time t while indices in
upper position stand for those at time t + At.
The extension of the calculations to three-dimensional configurations can
be done: the method used is a finite volume explicit method. The calculations
have to be run over a three-dimensional fluid domain discretized in small
elementary cells. Within each cell i (volume V h surface £,), the conservation
equations can be generalized:
|-| (F.F.C.) dF= | (F.F.C. flux) dZ (39)
ot J Vi hi
where F.F.C. (for flowfield characteristics) is either gas mass density, momen-
tum or energy.
In order to obtain the left-hand term in (39), F.F.C. is assumed to be
constant on each basic cell, leading to the following approximation:
where F.F.C., , represents F.F.C. at time t over cell i.
To calculate the second term of equality (39) which corresponds to F.F.C.
flux through the boundaries of the grid cell, we resolve the contact discontin-
uity problem with each cell adjacent to cell i using the method described in
the previous section.
152
Bernadette Gossant
These calculations are performed in a direction normal to each face of cell i.
The tangential components of the velocity are then not modified by crossing
a shock or an expansion wave.
This gives the characteristics of the fluid at that boundary: pressure,
normal velocity, tangential velocity, mass density and energy. The amplitudes
of various fluxes can then be explicitly computed at time t + At and in cell i
using:
F.F.C., + am = F F ,C. M + ^ £ (F.F.C. flux) dZ
Equation (39) being completed with the ideal gas state equation, the F.F.C.
values at time t + At can be explicitly calculated, based on the known values
at time t and on the “major values” (P, U, R , E) obtained from the
discontinuity analysis:
• in two-dimensions, to each of the four faces;
• in three dimensions, to each of the six faces of cell i.
The values of u 1 and u„ which are taken into account for the calculation at
this point are the normal components of the velocity vectors over the
boundary selected.
(d) Boundary conditions
The scheme description (eqn 39) shows that boundaries need to be
introduced in the form of mass, momentum, and energy fluxes crossing the
faces located at the boundary of the computational domain. Further data,
depending on the type of boundary met, are necessary to determine these
fluxes:
• In the case of an impermeable wall the velocity of the gases penetrating
into the cell must be zero at the boundary, i.e. U = 0. The determination
of P then requires the creation of a phantom cell characterized by the
values (u b p h p x ) satisfying the above condition. If (u n , p n , p u ) are the
values of the boundary cell, we see that the selection u* = — uff (where
the upper index N stands for the component of the velocity vector
perpendicular to the face), p, = p„, and p x = p n is a solution of the
problem.
• If the boundary corresponds to a symmetry plane of the propellant grain,
the calculations are handled in the same manner as for the impermeable
wall.
• In the case of an injecting wall two steps are necessary to determine the
various fluxes. First, the reaction of the wall is calculated as for the inert
wall. Second, the fluxes obtained are increased by the mass and energy
Solid Propellant Combustion and Internal Ballistics of Motors 153
fluxes resulting from the propellant combustion; the momentum flux
related to propellant combustion is assumed to be zero.
• If the boundary is located at the exit plane of the nozzle in the supersonic
jet zone, the simplest solution consists in extending the fluid domain a
little beyond this plane, and assigning to the phantom cell the same
F.F.C. values as those computed for the boundary cell. At the beginning
of the calculations, before the nozzle plays its full role, the condition is
identical, and consequently not very strict. Care must be taken that the
induced error is not spread in the whole internal fluid flow domain.
3. 2.4.2. Examples using the two - and three-dimensional
programs
In Fig. 14 a comparison between the calculated and experimental results is
shown for a two-dimensional plane case. The experimental set-up developed
by ONERA reproduces a configuration close to the combustion chamber of a
nozzleless rocket motor. Its porous walls are fed by a cold air flow (260 K)
sufficient to initiate a supersonic regime in the expansion region. Figure 15
illustrates the calculated results for a forehead FINOCYL type of propellant
grain.
3.2.5. Experimental determination of the
flow fie Id
The tests are performed to:
• determine the flowfield pattern in actual geometries;
• confirm results obtained through predictions. These tests are done on
models the geometry of which sometimes differs from the actual propel-
lant grains configurations; nevertheless they have the advantage of an
easier control of input parameters and of less complex boundary condi-
tions.
3.2.5. 7. Flowfield measurements
(a) Pressure measurements
Tests on steady flows do not require the use of transducers having a very
wide bandwidth. But to obtain correct measurements of the pressure level in
various locations in the flowfield, these pressure gages must be accurate even
for fairly high average levels.
154
Bernadette Gossant
Y Schematic of the set-up
Exit plane angle.
| Injecting parous wall ^^15" 1
i
20 t
iz .
480
XS 32^ Ss
Exit cone
Evolution of the pressure P/Po ratio along the symmetry axis
Fig. 4.14. Procne code. Comparison between prediction and experiment.
(b) Velocity measurements
The hot-wire technique [37] used to determine both the average value of
the velocity and its fluctuations (needed when evaluating the Reynolds tensor
components) is interesting for “clean” flows of cold gases (without particles).
Laser anemometry (used by ONERA) allows to examine the local velocity
field in cold gases, but it necessitates seeding the fluid with very fine particles.
(c) Temperature measurements
A manufacturing technique for thermocouples of short response time has
also been developed. This provides the possibility of measuring temperature
in the hot and corrosive gaseous environment of the combustion chamber.
Solid Propellant Combustion and Internal Ballistics of Motors
155
57.90
57.70 57.50 56.75
56.15
(10 6 Pa)
Fig. 4.15. Pressure distribution in a Fin.
(d) Visualizations
Visualization consists of providing a transparent viewport on an experi-
mental set-up in order to observe the flowfield during a test. This process is
used with cold and hot gases as well. At very high temperatures it is necessary,
however, to make sure that the viewport ablation is not able to distort both
the observation of the phenomenon and its progress.
3.2. 5. 2. Models for the determination of flowfield pattern
(a) Models for analysis of gap pressurization
Free-standing propellant grains exhibit a gap between the thermally
insulated metal case and the insulator surrounding the propellant grain.
During ignition the pressure inside this gap is not in equilibrium with the
presssure in the combustion chamber. Because of this pressure difference, the
propellant grain flattens against the case wall, causing an elongation of the
propellant grain and the appearance of non-isotropic compression stresses
which may affect its structural integrity, particularly in the case of cold firing.
The experimental model is made of a case in which a cylindrical center port
propellant grain is placed. The whole assembly is pressurized through an
external tank. This is a cold gas test. Numerous gages (pressure, gap
156
Bernadette Gossant
thickness) distributed along various generatrices, describe the model behav-
ior when it is subjected to a pressure rise at a given rate.
(b) Model for streamlines visualization
Several types of geometry can be tested. Figure 16 shows an example of an
axisymmetric model. A half-cylindrical propellant grain with axisymmetrical
slots, modeling the actual propellant grain configuration, is glued to a
viewport. Photographs reveal streamlines issuing from the slots: they experi-
ence a significant deviation when meeting the main central spout. In addition,
photographs show the occurrence of a burning rate faster at the downstream
bottom of the slots than anywhere else in the propellant grain.
(c) Analysis model for pressure field
The propellant grain for these models is axisymmetric, or three-dimen-
sional (FINOCYL). The locations of the various transducers are selected to
allow a local measurement of the pressure along the symmetry axes and the
burning surface.
The geometry of the chamber is specifically designed so that there are
significant pressure differences between the various measurement points. This
Visualization window
Nozzle
Propellant
Thermal insulation
Test motor Insulator Pressure
measurement
Fig. 4.16. Fluid flow lines visualization during firing of an axisymmetrical test motor.
Schematic of the experimental set-up.
Solid Propellant Combustion and Internal Ballistics of Motors 157
also explains why the model is fired under relatively high pressure (approxi-
mately 10 MPa), and why, in some cases, it is equipped with a central rod
used to increase the pressure differences in the chamber.
3.3. BALLISTICS MODIFICATIONS TIED TO THE INTERNAL
AERODYNAMIC FIELD
Performance increases of rocket motors have led to the development of
grains with high volumetric loading fractions. The resulting geometries often
have the disadvantage of reducing the port areas which, as a consequence,
increases the mass flow in the combustion chamber, particularly at the
beginning of firing. Experience has shown that, under these conditions, a
local increase in the propellant burning rate, causing a deviation from the
theoretical evolution of the grain burning surface, occurs at the beginning of
the firing. Figure 17 illustrates the evolution of the pressure obtained at the
front end of a long star-shaped propellant grain. It clearly shows the existence
of an over-pressure at ignition. This phenomenon, which is nowadays better
controlled, is sometimes desired to obtain the specified pressure envelope.
Considered for a long time to be undesirable, it must be precisely quantified
in order to determine its consequences on the structural integrity and the
evolution of the propellant burning area.
3.3. 1. Erosive burning phenomena
3.3. 1 . 1 . Determination of formulation sensitivity
A great number of researchers have developed testing equipment to
determine the burning rate of a propellant subjected to a hot mean flux
Fig. 4.17. Erosive burning of a star-shaped grain, diameter 203 mm, length
1000 mm.
158
Bernadette Gossant
parallel to its burning surface. Most of them used small test samples, shaped
like small thin plates, placed in the hot gas flow released by a gas generator
located upstream.
Various methods have been used to determine the burning rate of the
sample: X-ray photography, detection of the burning time through a photo-
multiplier, extinction to pattern the new surface of the partially-burned
sample, and high-speed photography through a transparent viewport.
Published research describes various set-ups. Razdan and Kuo [38], and
King [39] used a gas generator, placed upstream. In France, at ONER A and
SNPE, interesting test systems have been developed, based on the use of the
ultrasonic method. This method allows a direct and local measurement of the
burning front location and therefore, by differentiation, the rate of propellant
burning rate without perturbing the phenomenon. This system is illustrated
in Fig. 18; it includes a viewport making it possible to use several ultrasonic
transducers, as well as the use of large quantities of propellant. The latter
characteristics offer the advantage of conditions closer to the actual combus-
tion of propellant grains, without having to resort to a gas generator.
3.3. 1.2. Experimental results
The most important observations are [38]:
• The occurrence of an erosive phenomenon related to a threshold value of
the main flow. It is possible, for a large number of compositions, to
Fig. 4.18. Erosive burning experimental arrangement.
Solid Propellant Combustion and Internal Ballistics of Motors 159
determine one velocity threshold (or specific mass flow rate) beyond
which the propellant burning rate increase occurs. The lower the refer-
ence burning rate (value determined when there is no mean flow) the
greater its sensitivity to the main flow will be.
• For a given flow velocity the propellant sensitivity depends on the
pressure level. The experiments performed by Marklund and Lake [40]
show that, for the same flow velocity at the walls, the relative burning rate
increase grows with the pressure level. But if we consider the specific mass
flow rate instead of the flow velocity, we still find the trends previously
noticed with the variation of the propellant reference burning rate. The
higher the pressure, the faster the reference burning rate of the propellant
which then becomes less sensitive to the specific mass flow rate.
• Typically, the main flow temperature and chemical species have no effect:
— the sensitivity of a propellant composition is independent of the
nature of gases produced by the generator when the combustion
gases are non-reactive;
— the burning rate increase seems basically independent of the temper-
ature of the hot gases sweeping the propellant surface.
• The presence of certain formulation parameters may lead to a negative
erosive effect: this effect (burning rate decrease instead of increase) is
clearly observed with active binder compositions the basic burning rate of
which has already been increased by a ballistic modifier. Several possible
explanations are offered:
— decrease of the heat transfer at the surface caused by a “blowing” of
the chemical reactants in the boundary layer that modify the
transmission coefficients and the reaction rates:
— formation of a melt binder coating on the surface, caused by the
shear stress in the fluid;
— in some cases, destruction of the carbonized residue due to the
addition of ballistic modifiers in the propellant composition.
3.3.2 . Modeling of the phenomenon
3.3.2. 1. The basic models
To relate the value of the local burning rate to the gas flow characteristics
in the combustion chamber, various empirical or theoretical laws have been
advanced.
(a) The multiplicative law
r = r b (l + ku) or r = r b (l + kG)
(40)
160
where:
Bernadette Gossant
r h = ap n = reference burning rate of the composition;
k — constant;
u = average velocity of the.main flow, assumed to be one-dimensional;
G = p z u = specific mass flow rate of the main flow;
p % = density of the gases.
Likewise, with the introduction of a G* threshold of flow rate:
r = r b [ 1 + k(G - G*)] (41)
Green and Vilyunov proposed similar equations [40].
(b) The additive law
This type of law, expanded from research work done by Corner and
Geckler, was proposed by Boisson [41]:
r = r h + ku (42)
3.3.2.2. Detailed models
(a) Lenoir and Robillard model
Lenoir and Robillard [42] propose a description of the erosive mechanism
where the burning rate increase results from the heat transfer from the flow to
the burning surface. For a given pressure and an external flow, the new
propellant burning rate is calculated by adding an erosive component to the
reference burning rate. It is obtained from the energy equilibrium at the
surface:
a(T f - T s ) = p p r£L+ c p (T s - 7J)] (43)
where:
r e = erosive burning component;
L= heat resulting from the decomposition of solid into gas,
assumed null by Lenoir and Robillard;
T f , T s , 7] = respectively, flame, surface and initial temperature of the
propellant;
c p = propellant specific heat;
p p = propellant density.
The coefficient of heat transfer a is the Chilton-Colburn coefficient modified
by Rannie [41]. It accounts for the surface injection:
a = 0.0288 • c g • p • u • R e " x 0 - 2 • P ~ 2/3 •
-fi
pu _
(44)
Solid Propellant Combustion and Internal Ballistics of Motors
161
where:
c g = specific heat of the gases at constant pressure
R ex = Reynolds number, based on the axial position
p, u = respectively, density and velocity of the main flow
p g , v g = respectively, density and velocity of the gases emitted at the
injecting wall
P = constant
P T = Prandtl number
Taking eqns (43) and (44) into account, the new burning rate is implicitly
expressed by:
r = ap n + r e (45)
Some researchers [38] have modified this law:
• using a Reynolds number based on the diameter rather than on the axial
location;
• introducing a term representing the mechanical erosion (Osborn and
Burick);
• introducing, for catalyzed EDB formulations, an additional component
due to the plateau effect when it exists (constant burning rate whatever
the pressure level): Jojic and Blagojevic.
(b) Analytical models for boundary layer including the
burning mechanisms
Lengelle’s model [43]
The basic burning model used is Summerfield’s GDF model, which is
representative of composite propellant containing ammonium perchlorate.
With this model, which only takes into account a diffusion flame between the
oxidizing products (AP decomposition) and the combustible gases (binder
decomposition), and assuming the Lewis and Schmidt numbers to be close to
one, the burning rate is given by:
where:
M 1/3
( 46 )
c g = specific heat of gases;
T f , T s = respectively, flame and surface temperatures;
Q = energy necessary to heat the propellant and transform it into
gas;
p g , p p = respectively, gas and propellant density;
M = mass of a pocket of combustible gas;
162
Bernadette Gossant
p, a = coefficients representing, respectively, viscosity and turbulent
diffusion in the main flow.
Expression (46) was established taking into account the modification of the
transport properties of the fluid by the main flow. Consequently, the GDF
model leads to add to the reference burning rate of the composition, a term
related to the local flow pattern, as the height of the flame itself is not affected.
The term p • s/p in (46) is calculated from the integration of the equations
within a Couette flow boundary layer assuming a constant external velocity
independent of the downstream location. Based on the work of Marxman,
Lengelle writes the equation that gives the velocity profile (inside the
boundary layer) above a plane plate with a constant injection velocity at the
wall. Based on this profile, on the calculation of the momentum thickness,
and on the friction coefficient, Lengelle calculates the turbulent diffusion term
using PrandtFs mixing length assumption. This term changes within the
bounday layer. Lengelle suggests using its average value for the entire flame
height L. The relationship providing the propellant burning rate is written as
follows:
where:
r
Cg (Tf - TJ j>
Pp Q L L
8-3
10 2
(47)
+ =
ln(l + B)
B
1
a + 2
King’s model [44]
The mechanisms considered in this model are also representative of
composite propellants combustion, containing ammonium perchlorate. Two
flames are included:
• the premixed flame of the ammonium perchlorate, considered as a
monopropellant;
• the diffusion flame between the gaseous species produced by AP and
binder decompositions.
The burning rate, determined by the energetic balance at the surface, is then
given, without external flow by:
I Ri(T f0> - T s ) + X 2 (T, - T t y
Pp ’ Q L\ L di{{ + L kin _
( 48 )
where:
p p , Q = same definitions as for (46);
k x = thermal conductivity of the HC10 4 /NH 3 gaseous phase;
A 2 = thermal conductivity of the oxidizers/fuels mixture issued
from AP and binder decomposition;
Solid Propellant Combustion and Internal Ballistics of Motors
163
L
Diff 9
T fox = AP flame temperature;
T { = diffusion flame temperature;
T s = propellant surface temperature;
L, = AP flame height;
L Kin = parameters related to diffusion flame, respectively: height
due to the diffusion and to kinetics of reactions.
When expressing the various heights. King writes:
Al H 1 + 1 + A *P 2 rf Ap}
where:
(49)
A l9 A 2 , A 3 = constants depending on propellant and gases thermal
properties and on the propellant surface temperature and
heights corresponding to the various flames types;
p = pressure;
d A P = diameter of AP particles
In this model the action of the flow is taken into account through the
diffusion flame bending under the effect of fluid velocity; eqn (48) becomes:
r i pi (Tfo,-r,) W - 1 (50)
P p • Q |_ -^Diff • sin 9 4- L Kin J
where 6(<n/2) is the angle formed between the diffusion flame axis and the
burning surface.
The various physical properties used in eqn (50) keep the same value in the
case of an injecting wall. Angle is calculated from the velocity profile in the
boundary layer using a simple iterative process. Empirical equations, based
on Mickley and Davis’ experimental results, make it possible to express the
local fluid velocity as a function of transverse location above the propellant
surface, main flow velocity and velocity of the injected gases.
(c) Recent models
These models (Sviridenkov and Yagodkin in 1976, Razdan and Kuo [38],
Beddini [45]) solve the conservation equations for simple two-dimensional
configurations (plane plates, cylindrical channels) of constant port area. Far
from the wall, simplifying assumptions are considered [38]: the two-dimen-
sional flow is isentropic and the fluid is non-viscous, though this assumption
was not invoked in ref. [45].
Close to the wall the fluid behavior is more complex; terms related to
viscosity are included (taking into account the Reynolds tensions). These
researchers use the assumption that a turbulent flow field, when averaged, is
164
Bernadette Gossant
steady: each physical parameter consists of an average steady value and of a
term representing the fluctuation from the average value over time.
3.3.2.3. Practical applications
The so-called “standard grain” SNPE method was developed for the
purpose of a quick determination of the propellant erosive burning sensitivi-
ty. It consists of firings at fixed pressure of small star-shaped grains. These
tests are performed on grains of various length, therefore corresponding to an
evolution of the burning surface area to the port area ratio. Approximate
values of the erosive burning parameters of the composition tested (slope k
and threshold G* of eqn 41) are worked out applying King’s model [44],
when the propellant is a composite containing ammonium perchlorate. The
values are later refined to match as best as possible the pressure evolution
(Fig. 19).
4. Transient and Unsteady Burning Phenomena
In the previous sections the mechanisms involved during steady burning or
slowly evolving operation sequences of a solid propellant rocket motor were
discussed. On the contrary, the following section deals with phenomena
observed during transient or unsteady burning: ignition and burn-out
periods, unexpected development of pressure oscillations in the combustion
chamber or thrust modulation.
Fig. 4.19. Comparison between prediction and experiment. Using the first King’s
model.
Solid Propellant Combustion and Internal Ballistics of Motors
165
4.1. TRANSIENT BURNING
4. 1. 7 . Origin
Transient burning occurs when the pressure level in the combustion
chamber changes very rapidly with time. Assuming a stationary regime
(Section 2.2), the heat flux transmitted by the gaseous phase creates a thermal
gradient in the propellant close to the burning surface. The equilibrium
displacement caused by any pressure variation requires an adjustment of
thermal gradients in the gaseous and condensed phases. Characteristic times
are associated with each zone:
for the propellant:
for the gaseous phase:
where:
c l? Pi are, respectively, thermal conductivity, specific heat, and
density of the propellant (index p ) and of gas (index g) at
constant pressure
d p is the propellant heat diffusivity
The typical residence time associated with the gaseous phase is much smaller
than the corresponding time for that associated with the solid propellant.
Consequently, several cases may occur, depending on the time during which
the pressure level is changed.
• if r < r p no unsteady effect;
• if r % T p the thermal gradient evolution in the propellant is delayed
while the gaseous phase instantaneously adjusts itself to
pressure changes;
• if t % r g each burning mechanism is affected by the fast pressure
evolution.
4. 1.2. Models
Kuo et al. [46] have done a very clear presentation of the conservation
equations that need solving to deal with the general problem of unsteady
burning. Various types of models have been developed. They significantly
differ from each other by:
166
Bernadette Gossant
• the terms excluded or included in the conservation equations;
• the method selected to solve the governing equations.
4. 1.2 . 1. Models of dp/cfx type [47,48]
The gaseous phase of these models is assumed to be steady and the
unsteady heat equation resolution is simplified. These models provide the
following relationship for the instantaneous burning rate:
where:
(52)
r h = ap n = steady-state burning rate;
d p = propellant thermal diffusivity = parameter which depends upon
instantaneous pressure and propellant characteristics.
4.1.2. 2. Zei 'do vich-No vozhiio v mo del
ZeTdovich [49] assumes that during the unsteady regime the gaseous
phase instantly reacts. The heat flux at the propellant surface is found from
the steady analysis of propellant regression, avoiding a detailed and tricky
modeling of the gaseous flame zone.
Equation (3) gives the expression of the steady-state temperature profile
occurring in the propellant assuming no condensed phase reaction. The value
of the surface heat flux is then:
where:
, a dr
O = A
ps p dx
(T s , s - Tj)
(53)
d> p s = heat flux at the propellant surface;
X p = propellant thermal conductivity;
d p = propellant thermal diffusivity;
T s s = propellant surface temperature for the steady-state regime;
r h = propellant stationary burning rate.
In addition, the steady-state propellant pyrolysis and burning rate laws
(eqn 4), are assumed to be valid and the convenient relationship between
surface temperature, initial temperature, pressure and burning rate is then
established. The heat conservation equation relative to unsteady events can
now be solved by including the steady-state thermal flux expression at the
propellant surface using stationary data. Due to assumptions involved, this
method is not suitable for homogeneous propellants.
Solid Propellant Combustion and Internal Ballistics of Motors
167
4. 1.2.3. Models with flame zone description
These models [47,50] solve the conservation energy equations for the
gaseous zone to determine the heat flux value at the propellant surface.
Simplifying assumptions are used; combustion, in particular, is represented
by only one reaction. Assuming a uniform production rate for the flame
products, the KTSS model [47], used for heterogeneous propellants contain-
ing AP (diffusion flame), gives the following value for the unsteady heat flux
at the propellant surface:
dT 1 , f Vr
b?* 1
0) =
g,s
-J - e> l
(54)
where:
r = instantaneous burning rate;
r h = stationary burning rate = ap n ;
c p , p p = respectively, propellant specific heat and density;
b,k = steady-state pyrolysis law coefficients written as
r b = b(T StS - T t )k;
Q s = heat released by the superficial decomposition reactions.
4.2. IGNITION
4.2. 1. Propellant grain ignition — flame spreading
A pyrotechnical device is used to ignite the propellant. Hot gases and
particles supplied by the igniter heat the propellant surface by conduction,
convection and thermal radiation. This heat flux is sufficient for the propel-
lant surface to ignite in some scattered spots. Then the flame propagates, the
combustion reactions begin to be self-sustained, and the entire surface is soon
burning.
Equation (12) under certain assumptions expresses the pressure rise due to
the central bore gas filling, consequence of the propellant surface ignition.
When written as:
the left-hand side term becomes a linear function of time t. This offers the
possibility, together with pressure recordings to determine the flame propa-
gation time [51]. It also allows one to calculate the maximum pressure rise in
the chamber,
168 Bernadette Gossant
This equation demonstrates that, theoretically, the smaller n, the greater the
pressure rise.
The rate of flame speed is particularly important when the propellant grain
is very long, or when the internal configuration is complex. Barrere [52] has
worked out an equation for convective heat transfer to the propellant surface.
4.2.2. Experimental methods for ignition study
The ignition characteristics of the various propellant families are usually
determined by performing tests on small samples. Hermance [53] has
reviewed the various methods used.
(a) Ignition through conductive heat transfer
As a reminder, numerous experiments are conducted in a shock tube. In
this technique the propellant sample ignites under the sudden pressure and
temperature rise resulting from the shock wave.
(b) Ignition through convective heat transfer
Lengelle et al [54] describe a set of results obtained by submitting a
sample to hot gases produced by either an arc generator or a small motor
using a polybutadiene solid propellant.
(c) Ignition through radiative flux
At present the laser beam method is widely used. A C0 2 laser, emitting a
10.6 fim coherent beam and about 200 W cm -2 flux, is well suited for the
propellant ignition studies. This technology offers the possibility of selecting
a flux level independent of pressure level, chemical nature of ambient gases
and moisture level. In addition, the laser can be operated in a pulsed mode. It
is then possible to differentiate the self-sustained combustion sequence
occurring after ignition from possible dynamic extinguishment. However, the
laser ignition method has several drawbacks:
• absence of hot gases at the sample surface;
• sometimes deep beam penetration inside the propellant;
• a relatively slow increase of the surface temperature in comparison with
actual ignition events.
4.2.3. Thermal flux measurement [56]
The flux received by a surface can be total or selective:
Solid Propellant Combustion and Internal Ballistics of Motors
169
• to determine the total incident flux, the fluxmeter emissivity is, as much as
possible, close to one;
• to determine the flux actually received by the surface, the fluxmeter
emissivity matches the propellant one;
• to select radiative flux, a viewport is placed between the fluxmeter and the
heat source: its spectral characteristics are chosen to allow a good
transmission of the source radiant component and it also plays the role of
a protection against convective flux.
4.2.4 . Characterization of the various propellant
families
4.2.4. 1. Ignition delay — flux charts
Before ignition, the unsteady heat equation can be solved if the initial
temperature T(x, 0) or flux $(x, 0) fields are known. This equation is written:
87 -A —
dt p dx 2 (57)
x < 0, 0 < t < t ign
where t ign is the ignition delay under constant flux.
In the particular case where a propellant (initial uniform temperature 7]) is
ignited, and assuming that its thermal properties are independent of the
instantaneous local temperature, the following equations are obtained:
where:
T s = propellant surface temperature;
t s = dTJdt;
<& = flux incident to the propellant surface = A p d7/dx| 0 -
t = time;
T = propellant thermal effusivity;
T i = propellant initial temperature.
When the tests are performed under constant flux level, eqn (58) becomes
simpler:
2
T s (t) — = -==<b-t 112
y Jin
( 60 )
170
Bernadette Gossant
Representing surface temperature rise of the heated propellant, eqn (60) is
further verified during ignition:
T , ig n-T, = ^4>C (61)
V r7t
where T sign is the propellant surface temperature at ignition.
If, for a given propellant, ignition occurs at the same surface temperature
(T s . jgn ), regardless of the flux level, experimental results must align in the
(T s jgn — In 0) axis with a (— 1) slope value. Figure 20 shows that eqn (61) is
clearly verified, whatever the propellant family; but it must be pointed out
that the higher the ignition delay the lower the ignition temperature.
4.2.4.3. Modification of the ignition delay — flux charts
(a) Definition of the ignition delay (Fig. 21 )
Under an external heat flux the propellant starts to decompose. The
regression of its surface is observed. This event sometimes occurs simultan-
1 . Results from Bauer and Ryan: non-aluminized
polybutadiene propellant
2. ONERA Results : non-aiuminized
polybutadiene propellant (82 % AP)
10 '
10
3. Suh’s results : Extruded double-base (1060
cal/g)
4. ONERA results: E.D.B. (800 cal/g and 1100
, cal/g)
\5. SNPE results : Polybutadiene propellant
w (70 % AP, 16 % Aluminum)
^6. SNPE results : Aluminized advenced
w cross-linked energetic binder propellant
, (75 % filler)
Inert binder composite
propellants
Low flux T S ~570K
High flux T s ~ 690 K
Double-Base propellant
Low flux T S ~430K
High flux T S ~500K
1
10 100
Flux W/cm 2
Fig. 4.20. Ignition chart for different propellant families. Tests performed with CO
laser under continuous radiation.
Solid Propellant Combustion and Internal Ballistics of Motors
171
LU
1
H
o
<
LU
11
<
Q
<
CC
LL
O
(D
O
TRAVERSE OF IGNITION MAP AT
FIXED l 0 (DISCUSSED IN TEXT)
DYNAMIC
EXTINCTION
FOLLOWS
DERADIATION
SELF-SUSTAINING
IGNITION
UOO<
QQOtE
r SUBSTANTIAL
FLAME DEVELOPMENT
FAINT IR EMISSION
FROM GAS PHASE AND
SURFACE
„ GAS EVOLUTION
log of radiant flux INTENSITY, lo
(cal/cm 2 s)
Fig. 4.21. Different events occuring during ignition.
eously with a luminous reaction taking place even before the conditions for
sustained ignition are met (concentration of reactants, thickness of the
propellant heated zone). At this moment a sudden suppression of the external
flux leads to drastic extinguishment.
Flux pulses of variable duration are used with the “go/no go” technique to
obtain ignition maps and delimit the self-sustained burning region (L Id point)
on the delay-flux chart.
(b) Definition of a dynamic extinction region
Experiments performed on double-base propellants containing no ballistic
catalysts [58] have shown that, a long time after ignition, the propellant may
be extinguished by suppressing the external flux. These experiments demon-
strate the existence of a dynamic extinction limit, thereby determining a
region on the “ignition delay-flux” map where the combustion is self-
sustained after flux suppression (Fig. 21). They also show that this extinction
limit greatly depends, as opposed to the ignition limit, on the pressure level:
the higher the pressure, the larger the self-sustained combustion region. De
Luca [59] believes that this behavior can be generalized to all propellants.
(c) Effect of flux source
Several authors have published experimental results showing that the
nature of the flux has no noticeable influence on ignition events, provided
that:
172 Bernadette Gossant
• an effective flux is taken into account during tests performed under
convective flux, because of the flux level variation during propellant
heating;
• radiation penetration in the propellant is limited during radiative flux
tests.
(d) Effect of optical properties
Because propellant is not entirely opaque, a portion of the incident
radiation is absorbed deep inside the solid, thereby increasing the ignition
delay [60].
(e) Effect of pressure level
Although it does not influence the ignition delay value when the flux
intensity is low (< 10 Wcm -2 ), pressure variations significantly modify the
previous charts under high thermal fluxes: whatever the propellant family,
the higher the pressure, the lower the ignition delay.
(f) Effect of oxygen partial pressure
Experiments reported by Hermance [53] show that the ignition delay
decreases when the oxygen partial pressure increases. It appears that, with
low concentrations of oxygen, the binder nature has a significant influence.
4. 2. 5. Numerical simulations
Under a forced constant flux, and considering an initial temperature field
evenly distributed, numerical models can predict the surface temperature
profile before and after ignition, until a steady-state combustion regime has
been reached. The propellant surface regression is introduced into the
governing equations as soon as its surface temperature reaches a critical
value.
One of these codes, developed by ONERA, has been adapted for extruded
double-base propellants. A description of condensed phase reactions and
stationary primary flame is included. Another code has also been developed
for polybutadiene propellants. The Zel’dovich-Novozhilov method is used to
compute the incident flux at the propellant surface.
4.3. INSTABILITIES IN SOLID ROCKET MOTORS
4.3.1. Background
Combustion instabilities during a rocket motor operation are detected as
oscillations superimposed to the average pressure. Their amplitude depends
Solid Propellant Combustion and Internal Ballistics of Motors 173
on the firing conditions and they are always undesirable, even if they do not
all have catastrophic consequences:
• average pressure shifts modify the motor performance, including exceed-
ing specified limits; they sometimes lead to motor failure;
• heat transfers are intensified by pressure oscillations and induce such a
rapid degradation of inner parts (thermal insulation, nozzle) that in some
cases they are destroyed before burn-out.
• pressure oscillations create vibrations which are transmitted to the whole
motor case causing greater stress on it than expected.
4.3. 1.1. Origin of motor instabilities
The existence of numerous perturbation sources inside a combustion
chamber (small solid pieces ejected by the nozzle, inner jets confluence, etc.)
may be at the origin of the combustion instabilities. These perturbations
affect propellant combustion. The burning rate adjustment to the instanta-
neous pressure value triggers an oscillatory phenomenon, the frequency of
which may be close to one of the acoustic modes of the central port acting as
a resonant cavity. They can also be close to frequencies specific to the internal
flow pattern. Instabilities occurrence and feeding in a rocket motor are due to
the energetic balance between amplifying (combustion) and damping (con-
densed phase in gases, case vibrations, etc.) phenomena.
4.3. 1.2. Classification of instabilities
Two sets of phenomena are referred to as “instabilities.”
(a) Irregular combustion phenomena
Pressure oscillations, even extinction and reignition are observed. These
oscillations, of a few hertz, are in phase throughout the whole combustion
chamber. They are called “chuffing” or “L*”, or “non-acoustic low frequen-
cy” instabilities (NALF). They occur under very specific operating condi-
tions: at low pressure and small characteristic length L* (combustion
chamber volume to throat nozzle area ratio).
(b) Pressure oscillations matching cavity acoustic modes:
Two families of instabilities are observed:
• Longitudinal instabilities, matching the longitudinal modes of the cavity.
They are characterized by frequencies of a few hundreds of hertz and
moderate peak-to-peak amplitudes, sometimes associated to average
pressure shifts. They are typically observed on large rocket motors.
174
Bernadette Gossant
• Transverse instabilities, following the transverse modes of the cavity (in a
cross-section of the cavity); these are characterized by frequencies of a few
tens of kHz, high peak-to-peak amplitudes and generally sudden and
important average pressure shifts. They occur on small rocket motors
using non-metallized propellants.
4.3. 1.3. Determination of acoustic modes
Acoustic pressure field description is needed to predict instabilities occur-
rence. The wave equation is solved using classical acoustics assumptions
[33]:
(a) oscillation p' has a low amplitude compared to average pressure p ;
(b) absence of average flow;
(c) walls are rigid (the nozzle is acoustically closed):
S 2 p f
dt 2
d 2 -Ap' = 0
(where a = average speed of sound)
with the following boundary conditions:
Vp'-ri = 0
Computations in the case of simple geometries
When considering a closed tube as a first approximation of a simple
motor cavity, the solution is expressed by:
p ' = p(r, 0, z) • cos(cot + ip)
where p(r, 6, z) represents the spatial distribution of the mode (now
shortened as p).
For a stationary mode, we have:
P = A ■ J m g ™ n • cos (m 6 + (?) ■ cos ^-^ ( 62 )
L = length of the cavity;
D = port diameter;
d = considered diametral position;
a = average speed of sound in the gases;
m,n,q = arbitrary integers;
J m = Bessel function of mth order;
a mn = roots of dJ m /dr = 0 (tabulated values);
(p, \p — phase angles;
A = amplitude known with a multiplicative constant.
Solid Propellant Combustion and Internal Ballistics of Motors 175
Modes can be classified depending on m, n and q values:
m = 0 n = 0 <7/0 pure longitudinal mode
m/0 n = 0 <7 = 0 pure tangential mode
m = 0 n/0 <7 = 0 pure radial mode
Computations in the case of complex geometries
In the case of actual more complex propellant grain configurations
(machined grains or FINOCYL), longitudinal and transverse modes are
obtained by specific computer programs solving the wave equation in the
combustion chamber. Figure 22 illustrates this type of resolution for a grain
with axisymmetric slots; longitudinal acoustic modes are determined using a
finite elements procedure.
4.3.2. Unsteady combustion models
4. 3.2.1. Definitions
The purpose of this section is to identify the sensitivity of the propellant
combustion to the acoustic field (“pressure-coupling” effects) and to the
aerodynamic field (“velocity-coupling” effects).
Pressure-coupling
The propellant pressure-coupled response involves two major effects:
(a) mass flow rate response to pressure fluctuations:
Fig. 4.22. Axisymmetric propellant grain analysis. Grid and isopressure values.
176
Bernadette Gossant
(b)
mass flow-rate response to temperature fluctuations:
where:
Rjp —
P'/P
m\ p\ T are respectively maximum specific mass flow rate,
pressure and temperature fluctuations;
m,p, T f are respectively average values of specific mass flow rate,
pressure and flame temperature.
Fluctuations are mainly dependent on frequency and average pressure.
If the frequency is very low, specific mass flow rate response term is
equal to the pressure exponent of the steady-state burning rate law.
Velocity-coupling
In the linear range the specific mass flow rate response is defined by:
where:
Rmv ~
m/m
u' = unsteady normal component of gas velocity;
a = average speed of sound.
The velocity-coupling phenomenon is complex, depending on the average
velocity of combustion gases and acoustic velocity fluctuations. Unlike
pressure-coupling, the velocity-coupled response is not only a propellant
characteristic, since it also depends on the gas flow pattern inside the
chamber.
4.3.2.2. Models
Current models are one-dimensional and based on a description of the
combustion zone. Simplifying assumptions especially involve a homogen-
eously heated solid phase, a very small interface where the decomposition
reactions occur and a gaseous phase where combustion products react. The
following expression for the specific mass flow rate response has been
proposed by Culick [61]:
n *-A-B
X + (A/A) - (1 + A) + A - B
where:
X = complex function of frequency /;
n = exponent of the steady-state pressure law r — ap n ;
A and B = constants, worked out from physicochemical analysis
(activation energies, surface temperature).
Solid Propellant Combustion and Internal Ballistics of Motors 177
4.3.3 . "L* " instabilities
This chuffing phenomenon is characterized by pressure oscillations at very
low frequencies (a few hertz). Large pressure peaks and depressions are
generally observed:
• the amplitudes of pressure oscillations are inversely proportional to the
frequency;
• frequency increases with pressure;
• an increase of the motor characteristic length (L*) leads to a decrease of
frequency and of oscillations magnitude.
For the moment, only experimental methods enable the designer to predict
motor L* instabilities occurrence.
4.3.4 . Prediction of instabilities
4.3.4. 1. Background
Due to the complexity of phenomena, the methodology of instabilities
prediction has been split in two major steps:
• The first step is devoted to predict instability risks; it consists in
determining whether a perturbation will tend to grow (unsteady opera-
tion) or damp (steady-state operation); this analysis must be made for
each potential mode.
• The second step is run for each unstable mode. It consists in computing
limiting cycles amplitude as well as the magnitude of average pressure
shift. Theoretical approaches account for non-linear phenomena that, in
this case, drive instabilities growth.
4.3.4.2. First step: linear acoustic balance
Linear acoustic balance theory
Linear acoustic balance is the most widely used approach. The principles
of this method have been given and developed by Culick [62].
The fluid mechanics equations, written for the combustion chamber, and
the ideal gas state equation are linearized: small quantities, called “perturba-
tion parameters” such as the Mach number and the amplitude of the pressure
oscillations, are the new unknowns. The problem consists of seeking sol-
utions expressed in the following form:
p' = p • exp i(co — i<x)t = p • exp(i • a • k • t) (63)
where k is related to the frequency of oscillations ( co = Inf) and to the
coefficient a characterizing amplification or damping.
178
Bernadette Gossant
Mechanisms considered in the acoustic balance assessment will either
amplify the initial mode perturbation (combustion, turbulent flow) or will
tend to damp it (nozzle, two-phase flow, mechanical vibrations).
Consequently, various terms are summarized which form coefficient a and
express the contribution of each mechanism i:
« = Z “i
Detail of linear acoustic balance terms
(a) Gain resulting from pressure-coupling
This is written as follows:
where:
2 [ fir *V
JV
(64)
R = real part of the pressure-coupled propellant response;
M b = Mach number of the gases leaving the burning surface;
p n = shape of mode n (acoustic calculations).
Integrals are computed over the whole propellant burning surface S
(numerator) and the whole chamber volume V (denominator).
(b) Gain resulting from velocity-coupling
Culick expresses the gain resulting from velocity-coupling, in the linear
range, as follows:
a cv — 2
.[ ’ *,-A-VA-dS
J*
(65)
■dV
where R v is the imaginary part of the propellant velocity-coupled response.
(c) Gain resulting from the average flow rate and its
perturbations (vortex shedding)
Especially devoted to segmented configurations (propellant grains inde-
pendently mounted in a motor), Brown et a/.’s research [63] shows the
Solid Propellant Combustion and Internal Ballistics of Motors 179
nature of interactions between flow and acoustic fields. Vortices detach from
the aft end of one segment and impact on the following downstream segment.
A perturbation travels back through along the flow and can reinforce vortex
shedding effects. These experiments performed in cold gas channels revealed
the importance of Strouhal number S t , defined as:
S,=
fd
u
where:
/ = vortex shedding frequency;
d = characteristic distance;
ti = average flow velocity.
These experiments have demonstrated that coupling between chamber
acoustics and flowfield occurs when 0.2 < S t < 1. This law seems to be
correctly proven on actual rocket motors. The formulation of this contribu-
tion to acoustic balance has yet to be properly expressed and verified.
(d) Particulate damping
Because of their dynamic and thermal drags, particles distributed in gases
induce attenuation and dispersion of the pressure waves in the combustion
chamber. Culick [64] proposed the following expression describing the
damping capacity of spherical particles of diameter d :
1 C n
a ” 2 l + r
Oi 2 -X 6
[1 + co 2 -
Td +(y- 1) C
CO
C g 1 + CO
2 <
( 66 )
where r d = p s ■ d 2 /l 8 /i and z t = (3/2) (c s /c g ) P r • r d
are, respectively, the dynamic and thermal relaxation times, and
co = pulsation;
C m = particles mass ratio;
p s ,c s = respectively, density and specific heat of the particles;
p, y, c g = respectively, viscosity, specific heat ratio and gas specific heat at
constant pressure;
d = particles diameter;
P r — Prandtl number.
A very detailed knowledge of the particle size distribution in the combus-
tion chamber remains one of the main difficulties in making an accurate
particulate damping prediction. At present, calculations are done only on
rough estimations of this particle size distribution.
180
Bernadette Gossant
(e) Losses associated with nozzle impedance
These are written as follows:
«. = -
J (.4, + Af,)/>,‘ dS
JV
( 67 )
where:
M e = Mach number in the nozzle entrance plane;
A t = admittance of the nozzle in the same plane. The absolute value of
the upper integral is computed over this reference plane; the
absolute value of the denominator is calculated for the whole
chamber volume.
With longitudinal modes and short nozzles (entrance cone length 4,
wavelength) and assuming isentropic oscillations, we have:
In complex cases the nozzle admittance is numerically calculated.
(f) Visco-acoustic losses
The initial linear acoustic balance model does not take into account
viscous phenomena, which are of primary importance for the particles
behavior and appear close to the burning surface.
Culick suggested introducing the so-called “flow turning” effect for the first
time in 1973. Flandro’s approach [65] is based on a detailed analysis of the
fluid layer located near the burning surface. His method uses the notion of
admittance correction. Both approaches give very similar results when used
for simple propellant grains under strong flow conditions.
(g) Losses caused by the solid grain
This contribution requires additional calculation: the acoustic analysis of
the cavity is coupled with a vibration analysis of the propellant grain. At the
gas/solid interface, displacements are set to the same value, so that continuity
is ensured. Using experimental results for the propellant complex modulus it
becomes possible to evaluate structural damping.
Solid Propellant Combustion and Internal Ballistics of Motors 181
4.3.4.3. The second step: evaluation of oscillation amplitudes
and average pressure shifts — non-linear analyses
There are two kinds of approach:
• Exact methods, which strive to solve complete equations, are using
numerical procedures that are, at this time, very difficult to apply to
actual motors [66,67].
• Approximate methods which simplify the problem: the system of partial
derivative equations representing the motor operation is cast into a
differential equations system. This approach, proposed by Culick [68], is
the so-called “averaging” method, which has been successfully applied to
rocket motors with simple geometry.
4 . 3 . 5. L ongitudinal instabilities
4.3.5. 1. First step: linear acoustic balance
(a) Characterization of the propellant pressure-coupled
response
Indirect Methods
These methods are based on the propellant response determination from a
model and on the unsteady analysis of a test motor firing. Two types of
motors are widely used: self-excited or pulsed center- vented burners and
rotary valve or modulated exhaust burners.
T-Burner. The T-burner (Fig. 23) is a tube at the end of which two
propellant samples are placed (end-burning slabs or small slotted tubes) [64].
Fig. 4.23. T-burner schematic of the set-up.
182
Bernadette Gossant
The frequency is determined by T-length and average gas temperature. The
combustion products are flushed outside through a non-sonic center vent
toward a surge tank which maintains the T-average pressure roughly
constant during firing. The whole set-up is nitrogen pressurized before firing
in order to simulate the actual motor operating pressure. Various longitu-
dinal modes can be observed:
• self-excited operation mode: the term corresponding to pressure oscilla-
tions increase, a 1? is determined during firing, and after burn-out the a 2
term related to damping phenomena becomes available.
• pulsed operation mode: pressure oscillations are triggered during firing
by pulsers. They allow determination of the cn { terms describing the rate of
amplitude change of the driven oscillations. The difference a c = a x — <x 2
gives the combustion contribution related to the propellant pressure-
coupled response.
• Variable area T-burner: in this mode, obtained by using hollow cylindri-
cal sample with variable combustion area, the T-burner may exhibit
oscillations even with highly aluminized compositions.
ONERA modulated exhaust motor [69]. In his technique (PEM burner),
oscillations are driven in the combustion chamber during the whole firing.
The test motor includes an end-burning propellant grain, and a nozzle
limited to its entrance cone. A cog-wheel rotates in front of the throat area,
producing a partial modulation of the throat nozzle area and of the ejected
flow.
The propellant response is obtained by analyzing the pressure oscillations,
the throat modulation oscillations, and using an operational model of the test
motor. Figure 24 shows the pressure-coupled response of a propellant tested
in the SNPE T-burner and ONERA PEM motor.
• SNPE T-Burner
■ ONERA modulated exhaust burner
Fig. 4.24. Propellant pressure-coupled responses measured with modulated exhaust
and center-vented burners.
Solid Propellant Combustion and Internal Ballistics of Motors
183
Direct methods
Results obtained with the previous indirect methods are not very accurate.
This lack of accuracy is mainly related to model deficiencies as well as to
technical difficulties involved in test implementation.
To overcome these difficulties, studies have been undertaken in the United
States [70] and in France (at ONER A) in order to directly determine
fluctuations of specific mass flow rate induced by transient pressure fluctua-
tions. Fluctuation measurements in this case are based on the analysis of the
changes in the characteristics of a microwave frequency electrical wave
traveling through the propellant and reflecting on the burning surface.
(b) Velocity-coupling characterization
This is a delicate determination because of the difficulties met in designing
a test device in which the propellant would be affected only by acoustic
velocity oscillations. This phenomenon being always associated with pres-
sure-coupling, the intricate aspect of this characterization is enhanced by the
fact that the velocity-coupled response is very closely linked to internal
aerodynamics. It is necessary to make sure that the considered testing device
gives a valid reproduction of the internal flowfield pattern of the actual
motor.
(c) Linear acoustic balance assessment
Philippe and Tchepidjian [71] have developed a computer code based on
an analysis of linearized equations which performs the acoustic balance for
axisymmetrical motors. The input data are the parameters related to the
pressure coupling a c , average flow rate a e , nozzle impedance a t , particulate
a p , and structural vibrations.
Parametric studies performed with this code demonstrate that the most
significant terms correspond to pressure-coupling and particulate damping.
In order to account for experimental discrepancies and simplified assump-
tions (in particular, particle size distribution), the authors have defined the
following criteria:
• damping of considered acoustic mode when a < — 0.1 /;
• occurrence of the considered acoustic mode when a > + 0.1/;
• “critical” acoustic mode when —0.1 / < a < 0.1 /
4.33.2. Second step : non-linear aspect— limiting amplitudes
and average pressure shifts
Test results are obtained by firing star-shaped grains with a constant
burning area. When half of the web is burned, an impulse is triggered by
184
Bernadette Gossant
igniting a load of black powder located at the front-end of the propellant.
Under low average pressures, pressure oscillations damp: the rocket motor is
in a steady configuration. Under higher average pressures the pressure
perturbation grows and reaches a limiting cycle. In this case the chamber
average pressure is most of the time largely increased.
Tests performed at various pressures allow the determination of a thres-
hold pressure p s . Applied to a large number of polyurethane and poly buta-
diene propellants [72], they help to draw a pressure-burning rate diagram in
which pressure thresholds are located along a line that separates steady and
unsteady regions (Fig. 25).
This is a useful test for the classification of various compositions according
to their instability tendencies from a non-linear point of view. It is also used
to characterize the motor sensitivity to high-amplitude pressure and velocity
perturbations.
Fig. 4.25. Determination of steady-state and unsteady regions in a velocity versus
pressure plot.
Solid Propellant Combustion and Internal Ballistics of Motors 185
4 . 3 . 6. Transverse instabilities
4.3.6. 1. Experimental studies
Firings exhibiting transverse instabilities (generally tangential) are charac-
terized by high-frequency pressure oscillations and significant average pres-
sure shifts.
A special burner equipped with a viewing port has been designed in order
to observe combustion phenomena. The pressure level in the cylindrical
combustion chamber is recorded at several locations in one cross-section.
Tests performed demonstrate that the observed acoustic modes are unsteady
modes. Furthermore, random motions of nodal lines are observed: strong
rotations correspond with high pressure peaks.
43.6.2. "L/D" Method
At the origin of this method, a series of investigations [72] have been done
on simple grain geometries, and researchers varied the firing conditions to
determine an acceptable operation range (Fig. 26). They proposed a non-
linear criterion to compare the severity of the observed acoustic modes. This
criterion is defined as the ratio of the amplitude of the first pressure shift (A p)
to the stabilized pressure level p just before the shift. The motor operation is
said to be steady when A p/p is zero or small (a few per cent) and unsteady
when A p/p is high (several tens of per cent). It is a non-linear criterion.
(a) Effect of burning to throat area ratio K
With a given propellant, it can be noticed that pressure oscillations are first
driven by K growth. Then these oscillations rapidly diminish, becoming non-
existent beyond a threshold value K s (or threshold pressure p s ).
(b) Effect of length
While keeping a constant K value, increase of the propellant grain length
(without varying its port section) leads to unsteady effects beyond a threshold
length L s .
(c) Effect of initial diameter
By varying the propellant grain length for different values of the initial
diameter, we observe:
• The existence of an L/D threshold, beyond which pressure oscillations
occur. This threshold value varies from 5 to 10 depending on the
propellant composition.
186
Bernadette Gossant
Criterion for instabilities
severity
Effect of K ratio or
pressure values
Effect of length
1
d
Influence of initial diameter
1 i
Is
Unstable region
Stable region
d
Fig. 4.26. Research of a steady-state operation range.
• In some cases the existence of a critical diameter, below which motor
firings are always instability-free.
4.3. 6. 3. Acoustic balance
Few studies have been done on this method in the field of transverse
instabilities, because of the lack of experimental evaluation for the propellant
response function at these high frequencies.
Lovine [74] has described a slotted T-burner. Its small dimensions make it
possible to obtain frequencies up to 13 kHz. Kuentzmann et al. [75] have
developed a motor with a partially modulated nozzle throat. Response
measurements between 3 and 15 kHz are obtained within one firing, which is
due to the geometrical evolution of the propellant grain.
Solid Propellant Combustion and Internal Ballistics of Motors 187
4 . 3 . 7. Suppression of instabilities
There are two ways to cancel instabilities:
• the first consists of adjusting the propellant grain shape;
• the other consists of tailoring the propellant (production of particles that
damp oscillations during combustion).
Implementation of these solutions is never easy. The solutions require design
testing, and improvements are always obtained at motor performance
expense.
4.3. 7. 1. Propellant grain geometry
(a) Helmholtz resonator
This is a small cavity linked to the combustion chamber through a throat.
It must be located at a vibrational antinode and tuned to the frequency that
needs to be damped. This device has been used several times to stabilize
longitudinal modes.
(b) Resonance rod
This device is widely used. It consists of a rod embedded at the forward end
of a rocket motor; it fills a portion of the central port length. Rods with
rectangular or cruciform sections are the most efficient. They prevent gas
rotation and suppress pressure peaks, particularly at the beginning of firing.
(c) Longitudinal baffles
These are small plates placed lengthwise inside the propellant grain.
During combustion, they emerge inside the combustion chamber and create
obstacles that block the rotation of the gases.
4.3. 7.2. Propellant composition
The addition of a low particle content, as ingredients in the propellant, is a
method often successful in stabilizing motor combustion. This is particularly
true in the case of tangential instabilities. Once the frequency that needs to be
damped is known, it is possible to theoretically predict, depending on the
particulate nature, the most efficient particle diameter [76]. This first
estimation is very helpful in selecting size distribution of commercial prod-
ucts.
The actual problem is in fact much more complex, because there is often
not one frequency, but a large frequency range that needs to be stabilized, and
188
Bernadette Gossant
the products used never exhibit a single diameter. Aluminum has been used
for quite a long time; because of the lack of control on the alumina particles
diameter that are produced in the combustion gases it is impossible to reach a
maximum damping. Therefore, researchers have made new attempts with
inert products, the high melting point of which gives the possibility of
damping effect optimization with low particle amounts. This solution has the
additional advantage of not affecting the rocket motor signature.
With an average particle size ranging from 1 to 2 /mi, these products
provide good damping for frequencies of the order of 15 kHz.
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29. Beckman, C. W. and Geisler, R. L., Ballistic anomaly trends in subscale solid rocket
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31. Boggs, T. L., Zurn, D. E. and Derr, R. L., The effects of strain on the burning rates of high
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32. Plantif, B., Influence of acceleration on the combustion of solid propellants, measurement
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33. Boisson, J., La propulsion par fusee . Cours de 1’Ecole Nationale Superieure des Techniques
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36. Godounov, S., Zabrodine, A., Ivanov, M., Kraiko, A. and Prokopov, G., Resolution
numerique des problemes multidimensionnels de la dynamique des gaz. Editions Mir-Moscou,
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37. Asch, G., Charnay, G. and Schon, J. P., Capteurs de vitesse, debit et niveaux de fluide. Les
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38. Razdan, M. K. and Kuo, K. K., Erosive burning. Fundamentals of Solid Propellant
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41. Barr£re, M. and Larue, P., Contribution a 1’etude de la combustion erosive des poudres
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42. Lenoir, J. M. and Robillard, G., A mathematical method to predict the effect of erosive
burning in solid propellant rocket. Sixth International Symposium on Combustion, Reinhold
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45. Beddini, R. A., Analysis of injection-induced flows in porous walled ducts with application
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47. Krier, H., T’ien, J. S., Sirignano, W. A. and Summerfield, M., Non-steady burning
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49. Summerfield, M., Caveny, L. H-, Battista, R. A., Kubota, N., Gostintsev, Ya. and
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56. Guernigou, J., Indrigo, C., Maisonneuve, Y. and Mentre, P. G., Mise au point de
fluxmetre a temperature superficielle, La Recherche Aerospatiale, No. 3, pp. 159-168, 1980.
57. De Luca, L., Caveny, L. H., Ohlemiller, T. J. and Summerfield, M., Radiative ignition of
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58. Ohlemiller, T. J., Caveny, L. H., De Luca, L. and Summefield, M., Dynamic effects on
ignitability limits of solid propellants subjected to radiative heating. Contract AFOSR-69-
1651-BRL, 14th International Symposium on Combustion, Combustion Institute, Pittsburgh,
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additional source of acoustic energy in segmented solid propellant rocket motors. AIAA 80-
1092, AIAA/SAE/ASME 16th Joint Propulsion Conference, 1980.
Solid Propellant Combustion and Internal Ballistics of Motors 191
64. Culick, F. E. C. (Editor), T-Burner testing of metallized solid propellants. AFRPL.TR.
74-28, 1974.
65. Flandro, G. A., Solid propellant acoustic admittance corrections, Journal of Sound and
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389-415, 1973.
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moteurs fusees a propergol solide. AGARD CPP No. 259, Solid Rocket Motor Technology,
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Astronautica , 3, 715-757, 1976.
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pression et de vitesse, Combustion Science and Technology , 11, 119-139, 1975.
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determining solid propellant transient regression rates, Journal of Spacecraft and Rockets ,
11,75-83, February 1974.
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axisymmetrical propellant grains. AIAA 84-1358, AIAA/SAE/ASME, 20th Joint Propulsion
Conference, 1984.
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fusees a propergol solide. Colloque sur la combustion des propergols solides , Poitiers, 1972,
Cahiers de la Thermique, No. 4, Serie B, pp. 35-40, May 1974.
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rocket motors. Solid Propellant Rocket Research Conference, ARS Paper 1067, 1960.
74. Lovine, R. H., High frequency propellant response measurements. AIAA 77-976, AIAA/
SAE/ASME, 13th Joint Propulsion Conference, 1977.
75. Kuentzmann, P. and Laverdant, A., Determination experimentale de la reponse d’un
propergol solide aux oscillations de pression de haute frequence, La Recherche Aero-
spatiale , No. 1, pp. 39 55, 1984.
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damping in smokeless solid propellant motors, AGARD CPP No. 259, Solid Rocket Motor
Technology , pp. 27.1 27.10, 1979.
CHAPTER 5
Plume, Signal Interference and
Plume Signature
GERARD PRIGENT
1. Introduction
The presence of a plume with attendant radiation and smoke at the aft end
of a missile, due to the combustion and pyrolysis products of the rocket
motor exhausted through the nozzle, may cause a missile to fail in its mission.
The plume or smoke may reveal the launch location of a missile and allow
the missile to be located in flight. In the case of missiles guided optically (at
visible or infrared wavelengths), the transmission of commands through the
plume or smoke trail may be substantially attenuated, leading to the loss of
control of the missile. Intense flames at the rear of the missile, caused by
combustion of the motor exhaust products with air (afterburning), may also
reveal the launcher location and trajectory of the missile.
The flames may also cause saturation of the instruments used for optical
tracking of the missile or of the target. The flames increase the temperature of
the plume, resulting in increased emission of infrared radiation. In addition,
the transmission of radar frequency electromagnetic waves is generally very
weakened by absorption by these flames that contain ionized species. The
flames have also been known to cause engine flameout of jet aircraft that
launch the missiles, and also damaging impingement effects on launcher
surfaces.
Finally, the nozzle exhaust products may often cause a disturbance of the
thrust vector control components because of slag or erosion.
The principal methods used to guide and control missiles [1,2] new ref
usually require links between:
• the firing station and the missile;
• the firing station and the target;
• the missile and the target.
193
194 Gerard Prigent
The nature of these links may vary:
• optical links (visible or infrared), the wavelengths most used in infrared
are 0.9, 1.06, 10.6 /im;
• electromagnetic links (radar);
• electrical links with conductive wires.
As for the detectability (or signature) of a missile, there are several factors
intervening, such as the contrast of the plume and smoke trail [3] against
various backgrounds and under various types of lighting, and the emission of
visible and infrared radiations by the gases and hot particles that make up the
plume.
The purpose of this chapter is to describe (1) plumes and plume phe-
nomena, (2) interactions of plumes with the links necessary for guidance
and the means of detection, and (3) means to diminish or suppress these
interactions. Therefore this chapter includes:
• a physicochemical analysis of the plumes and smoke trails;
• a description of the methods available to determine the physicochemical
characteristics;
• a presentation of the methods available to predict the properties of the
plume and smoke trail;
• an examination of the influence of the characteristics of the rocket motor
(operating conditions, nature of the propellant, inhibitor, liner, and
insulation materials, etc.) on the nature and the properties of the plume
and smoke trail;
• methods to eliminate or minimize some of these undesirable characteris-
tics in terms of guidance and signature.
2. Description of the Flow Exiting from a Nozzle
2.1. BACKGROUND
The flow at the exit plane of the nozzle of a solid propellant rocket motor in
operation is supersonic, with an average temperature of the mixture of gases
and solid or liquid particles generally over 1000 K. The local pressure may be
greater, lower or equal to the atmospheric pressure, and the flow is said to be,
respectively, under-expanded, over-expanded or matched (optimum expan-
sion).
Downstream from the nozzle, the hot portion of the flow is commonly
called the plume. Various phenomena, such as turbulence, electronic excita-
tion, ionization, and most important, afterburning, occur in the plume.
The plume gas dynamic structure, as shown in Fig. 1, must take into
account not only the existence of discontinuities both in the velocity (slipline)
and the pressure (straight or oblique shocks), but mixing with the ambient
air.
Plume, Signal Interference and Plume Signature
195
1 . Outside flow
2. Nozzle flow
3. Outside limit of base flow
4. Inside limit of base flow
5. Outside flow of plume
6. Inside flow of plume
7. Recirculation zone at the base Boundary of jet in
non-viscous case
Base zone
Fig. 5.1. Diagram of the zones of the plume of missile in flight.
Condensed exhaust products, solid or liquid, may be present downstream
of the nozzle exit plane, leading to the presence of plume smoke, called
primary smoke. Secondary smoke may develop, further downstream and in
external regions of the plume, depending on the atmospheric conditions,
caused by the condensation of water vapor from both the plume and the
atmosphere.
The attenuation of radar waves and infrared emissions are more important
in the plume, and the absorption and scattering of visible light are more
important in the smoke trail.
Most of the chemical products in the plume come from combustion of the
propellant. Additional contributions to the exhaust gases and particles come
from thermal and mechanical erosion, pyrolysis and combustion of the
inhibitors, liners and insulators, and from ablation of nozzle and blast-tube
materials.
2.2. THE GASEOUS PRODUCTS
The major gaseous products contained in the combustion residue mixture
are nearly always CO, C0 2 , H 2 , H 2 0 and N 2 . Propellants containing
ammonium perchlorate produce, in addition, hydrochloric acid HC1
(Table 1).
The reducing power or fuel index of a gaseous mixture is usually character-
ized by the sum of molar fractions of hydrogen H 2 and of carbon monoxide
CO.
P — N co + N H2
196
Gerard Prigent
Table 1 Major combustion products from typical propellants calculated
N%*
Condensed
products* 3
Composition
HC1
CO
co 2
H 2
h 2 o
N 2
T b (K)
EDB
0
38
13
10
23
12
1.5
2630
Smokeless
EMCB
(NC, Ngl, RDX)
0
34
12
10
23
19
2775
Butalite
(HTPB + AP)
17
18
8
12
36
9
0.2
2798
Butalane
16
22
1.3
31
11
8
10
3620
a Molar fractions inside the chamber.
b Combustion temperature inside the chamber.
c Total fraction of the condensed particles at the exit plane of the nozzle after equilibrium
expansion.
This value, always somewhere between 0 and 1, is obtained by analyzing
the composition of the gases inside the combustion chamber (Chapter 3).
Assuming that the gaseous mixture in the combustion chamber is in
thermodynamic equilibrium, the reaction
(1)
CO + h 2 o +± co 2 -f H 2
( 2 )
is sufficient to provide an initial approximation to the respective amounts of
the mixture’s principal ingredients. The reducing power of the few propellants
used as examples in Table 1 ranges from 0.3 and 0.55. With composite
propellants it decreases when the ammonium perchlorate level increases, and
it increases with the level of HMX and aluminium. With EDB and CMDB
propellants it usually varies conversely with the combustion chamber tem-
perature. When the mixing of the combustion residual products with air is
accompanied by afterburning, the level of C0 2 and H 2 0 and the tempera-
ture, increase significantly.
2.3. PRIMARY SMOKE
Primary smoke consists of a mixture of liquid and solid particles usually
exhausted at the exit plane with the combustion gases. It is easily detected
because it exhibits the triple capacity of, at the same time, absorbing, emitting
and scattering ultraviolet visible, or infrared radiation. The corresponding
optical magnitudes depend on the number, size and nature of the particles.
The smoke may come from the pyrolysis of the inhibitor, the thermal
insulation, or from any other parts of the motor that come into contact with
the combustion gases, as well as from the propellant itself, which may contain
Plume, Signal Interference and Plume Signature 197
ballistic catalysts, anti-instability additives, and flash suppressors with min-
eral elements or reducing metallic fuel solids. It may also sometimes originate
directly in the combustion chamber as in the case of alumina, which is liquid
at a temperature over 2315 K, or of zirconium oxide, which solidifies as soon
as the temperature drops below 2990 K.
Other chemical products condense further beyond the throat of the nozzle.
Lead, copper, potassium and their oxides, for example, produce submicron-
size particles. From an attenuation point of view, these particle sizes result in
absorption and scattering of visible and infrared light which are very notable.
Carbon and soot particles constitute a special case. They are primarily
caused by the pyrolysis of materials of the chamber (liners, insulators, etc.).
Their size increases as a function of the residence time in the combustion
chamber [4]. Their size at the nozzle exit remains small, between 10“ 1 and
10“ 2 fim , contributing significantly to the signature of the plume, particularly
at shorter wavelengths.
End-burning grains that are inhibited on the lateral face produce a
significant amount of this type of primary smoke. It has been demonstrated
that the polyester inhibitor, having lost 3% of its mass due to heating by the
combustion gases of a CDB propellant (reducing power 0.6, combustion
temperature 2000 K) is enough to produce 1% (in mass) of soot in the smoke.
This quantity is sufficient to make the smoke trail of a missile detectable.
2.4. SECONDARY SMOKE
The combustion of propellant containing ammonium perchlorate (Buta-
lite, reduced smoke Nitramite) produces hydrochloric gas. Under specific
atmospheric conditions of temperature and humidity (Fig. 2) the combina-
tion with air results in the formation of a mist of azeotropic liquid drops of
H 2 0 and HC1.
It is observed that it usually takes several seconds for the secondary smoke
cloud to reach maximum opacity (Fig. 3). Increases of the absorption and
scattering of the visible and infrared light occur simultaneously, due to the
growth both in number and size of the drops.
In the case of composite propellants, with ammonium perchlorate contents
greater than 60%, the secondary smoke forms a very dense fog.
In contrast, the smoke observed during the firing of a XLDB (high-energy
binder + HMX) propellant with a low ammonium perchlorate percentage is
translucent, and difficult to differentiate from the primary smoke due to some
additives.
The importance of the secondary smoke depends on the operational
climatic environment of the missile. Table 2 compares the frequency of the
occurrence of secondary smoke for two propellants based on climate
variations (according to statistics provided by the French National Weather
Bureau).
198
Gerard Prigent
Fig. 5.3. Growth kinetics of a trail of secondary smoke in a climatic chamber
(600 m 3 ). Transmission versus time.
Plume, Signal Interference and Plume Signature
199
Table 2
Season
Frequency of occurrrence of secondary smoke
in Paris Montsouris (percentages)
82% AP composite
15% AP XLDB
Spring
30
17
Summer
19
4
Fall
50
25
Winter
64
40
Annual average
40
21
2.5. PLUME AFTERBURNING
Since the specific impulse of a propellant is inversely proportional to the
square root of the molecular weight of the gases, it is more efficient, from the
standpoint of thrust, to select a fuel-rich propellant whose combustion
produces an underoxidized (less than stoichiometric) gaseous mixture with
more carbon monoxide molecules than carbon dioxide, and more hydrogen
than water, and thus a relatively high reducing power. Theoretically, we note
the reducing power varies relatively little during the expansion through the
nozzle, so that downstream of the exit plane the gases are likely to burn again
when they mix with atmospheric oxygen. This phenomenon is called after-
burning or secondary combustion of the plume.
The motor exhaust flow, the design of the base of the missile, the speed of
the missile, the altitude, the pressure of the combustion chamber, and the
expansion ratio of the nozzle exit plane are some of the variables that, like the
reducing power and the temperature of the gases, affect the probability that
afterburning will occur, and at the same time, influence the ignition point and
the position of the flame in the exhaust flow downstream of the nozzle.
Afterburning is a complex phenomenon, and its parametric study is made
very difficult because the influence of the various parameters is not additive,
and because of their interactions within a complicated flowfield, typified by
Fig. 1.
Afterburning causes a temperature increase in the plume with resulting
increases in luminosity, infrared emission, concentration of ions and free
electrons (which increases radar attenuation and radar cross-section). After-
burning also increases the turbulence of the plume and, consequently, the
interference and defocusing of guidance laser beams, and the noise imposed
on radar guidance signals. The acoustic noise of a rocket motor is also
increased by afterburning. Afterburning may also modify the nature and
quantity of primary and secondary smoke.
200
Gerard Prigent
Because of the very high temperatures and high flow velocities in the areas
where afterburning is triggered, validation of theoretical values of these two
parameters by experiments presents serious technical difficulties.
It is easier, although somewhat uncertain, to validate theory by measuring
effects induced using the methods described below.
3. Description of the Methods Used to Measure
the Characteristics of the Plume and Smoke
The experimental methods developed have as a main objective the study of
phenomena induced by the flow of the gas-particle mixture of the plume and
smoke.
Firings generally take place on static benches, and projecting the measure-
ment values to the real case of a missile in flight involves risky extrapolation.
The static test results therefore most often serve to classify the propellants
tested for the optical phenomenon under study. Greatly different results may
occur in flight, as predictable with appropriate computer programs.
3.1. MEASUREMENT OF THE RADAR ATTENUATION
The presence of alkaline or alkaline-earth metal vapors, often just as traces
(a few tens of ppm) in the combustion gases, causes significant ionization of
the medium when the temperature is sufficiently high (T > 2000 K). This
situation occurs in the combustion chamber of the rocket motor and in the
afterburning region of the plume.
Free electrons subjected to the excitation of a radar wave with a frequency
of several gigahertz traversing the medium begin to vibrate. A portion of the
energy picked up is later dissipated in the plume through collisions with the
more massive gas molecules in the plume (N 2 , such as HC1, 0 2 ). The energy
lost from the wave, known as attenuation, is measured in decibels, using the
formula:
A = —\0 log j-
* e
where 7 e is the intensity of the incident wave and 7 r the residual intensity of
the wave after absorption by the plume.
The attenuation value depends not only on the frequency of the radar
wave, but also on the characteristics of the ionized medium traversed
(electronic density, collision frequency, etc.) [5].
For the purpose of simply comparing propellants, the attenuation is
usually measured transversely (that is perpendicular) to the axis (Fig. 4). This
measurement is not directly comparable with the measurements obtained by
a control station when the missile is in flight. For this reason a second type of
Plume, Signal Interference and Plume Signature
201
Fig. 5.4. Attenuation measured perpendicularly to the axis of a rocket motor for two
different propellants.
device is used to measure the attenuation as a function of the sighting or
aspect angle 6 (Fig. 5), known as a longitudinal or diagonal measurement.
For any specific propellant there usually is a ratio of 6 to 10 between the
maxima of attenuation obtained by longitudinal and transverse methods
unless the plume electron density is so high that non-linear effects, such as
refraction and diffraction, modify the longitudinally measured radiation.
3.2. OPTICAL TRANSMISSION IN THE VISIBLE AND
INFRARED RANGES
As examples, two methods of measurements used to study the optical
phenomena related to the occurence of smoke will be described:
• measurement made with a “smoke meter”;
• measurement on a free plume.
0 Degree
Fig. 5.5. Attenuation measured longitudinally.
202 Gerard Prigent
3.2.1. The smoke meter
The smoke meter is a subsonic wind tunnel, 10 m long and 1 m in diameter,
in which static motor firings are made to compare various propellants under
standard conditions by measuring the transparency of their primary smokes.
The optical measurements are made at the exit of the wind tunnel (Fig. 6),
with dilution of the exhaust flow between 10“ 1 and 10” 2 expressed by the
ratio of the respective flow rates of the motors and the air drawn into the
wind tunnel.
The major drawback is that the device is not very representative of the real
conditions under which smoke is formed. Furthermore, it does not allow the
study of firing with a short burning time (less than 2 s). But the measurements
are little influenced by the perturbations of outside climatic conditions, and
therefore are easily reproduced.
3.2.2. Free jet measurements
The test site for free jet firings must be protected from wind, and be
sufficiently spacious so as not to disturb the shape of the smoke trail.
A stationary measurement of the transmission is made, perpendicular to
the axis of the trail, in an area located downstream from the exit plane where
all primary smokes are usually condensed. A non-stationary (source and
sensor moving parallel to the trail axis) measurement allows estimation of the
rate of build-up, settling, and dissipation of the smoke trail behind the motor
of a missile versus time. A longitudinal measurement may be made instead.
Fan
Fig. 5.6. Absorption measurement at exit of smoke measurement device, (t;) is the
time needed to reach a stationary flow in the duct).
203
Plume, Signal Interference and Plume Signature
3. 2. 3 . Optical instruments
The instruments used to measure the transmission, through the smoke
trail, consist of an emitting source and a detector. The transmission level is
given as the ratio of the intensity received by the detector during the firing to
that before or after the firing.
The selection of the source and the detector depends on the range of
wavelengths in which the measurements are to be made. The range is
always located within the limits where the atmosphere is transparent.
3.3. MEASUREMENT OF INFRARED EMISSION BY A PLUME
The plume of a rocket motor is a source of heat, similar to an infinite
number of point sources emitting a radiation characteristic of the tempera-
ture and of the local concentration of chemical products, either gaseous or
condensed.
The resulting total emission is not the sum of the point sources because for
each emitting point a portion of the radiation is partially absorbed or
scattered by the other points in the vicinity.
The emission spectrum of a plume, whose maximum intensity is in the
short to mid-infrared wavelengths, is the superposition of a continuum of
particle radiation and radiation manifesting the vibration-rotation or rota-
tion-only types of radiation transfer (emission, absorption and scattering)
phenomena, of the gas molecules thermally excited.
An increase in the temperature in a plume, and chemical changes of the
mixture such as occur with afterburning, cause a corresponding increase of
the total intensity and a change in the spectrum of the radiation.
The use of an infrared camera (thermal imager) has allowed assessment of
afterburning; in particular, the verification of the efficiency of some flash
suppressors compounds in a smokeless propellant, by comparing the inten-
sity radiated by the plume from a modified propellant composition to that of
a propellant containing no such additive.
4. Description of the Methods of Analysis
The modeling of the physicochemical phenomena occurring downstream
of the exit plane of the nozzle required the development of computer
programs to simulate both the flow and chemistry of the gas-particle
mixture, and the optical phenomena tied to the plume or the smoke
trail.
204
Gerard Prigent
4.1. THE FLOW PROGRAMS
4. 1 . 1. Analysis of the flow of a plume
The results of the analyses of the properties of a plume depend on the
simplifying assumptions used to solve the Navier-Stokes equations, as well as
on the types of measurements on which the comparisons with theory are
based. Two types of models and computer programs are generally used when
there is a possibility of afterburning.
In the zone close to the base of the missile where there is a confluence of the
nozzle flow and the flow of external air behind the nozzle exit plane, and up to
a distance of 10 nozzle radii, the program used will calculate the three
characteristics (Fig. 7); pressure, temperature and velocity, as well as the
chemical composition. This program can be used for the large pressure
gradients that occur in this region. To reduce computer run times, simplified
chemical reaction schemes are often used; for example, use of reactions
involving only five gaseous products (CO, C0 2 , H 2 , H 2 0, 0 2 ) is often
adequate.
Further from the nozzle exit plane, a satisfactory description of the plume
can be obtained by using a computer program [6] assuming a constant
pressure in the plume, thereby allowing the use of a more sophisticated set of
chemical reactions. In particular, it is accepted that, in spite of the notorious
imprecision of some values of the rate constants in reactions that give rise to
free radicals, only a flow model using a chemical reaction system, such as the
system recommended by Jensen [7], affords the possibility of correctly
assessing the afterburning phenomenon [8]. More complex computer pro-
grams calculate pressure fluctuations of the plume with a full reaction set [9].
The ability to predict the plume with a computer program is fairly limited
in the case of weak afterburning [10,11]. The discrepancy between the
computer model and reality is probably related to imprecisions in the kinetic
model used in the computer programs, as well as to the fact that the
fluctuations due to turbulence are not taken into account in the calculations
of the chemical reactions in the plume. These two points are currently the
subject of many studies.
4. 1.2. Analysis of a flow in a smoke trail
Much further downstream from the nozzle exit plane, the combustion
products have cooled down, the gases are diluted, and all chemical products
likely to condense in the ambient temperature form a trail of smoke which
shows the flight trajectory of the missile. The trail of condensed water vapor
left behind by a jet plane is caused by the same phenomenon.
A computer program can calculate temporal evolutions of the temperature,
the velocity, and the dilution in each location of the trajectory, taking into
Plume, Signal Interference and Plume Signature
205
2
Nozzle exit plane
Fig. 5.7. Pressure field in a plume..
account the flight characteristics of the missile (direction, speed), the atmo-
spheric conditions affecting the rapidity with which the trail dissipates (wind
velocity, ambient temperature), and the characteristics of the residual pro-
ducts ejected by the nozzle (temperature, velocity, condensable fraction).
As an example, the modeling of the smoke trail may be based on the one-
dimensional flow, using an empirical law of dilution of the combustion gases
with the air along a specific trajectory of a missile [12]. The input data
include the velocity, the temperature and the composition of the gases and
size and number distribution of particles exiting the nozzle.
206 Gerard Prigent
4.2. THE OPTICAL PROGRAMS
Calculations of physical values such as the emission, absorption, transmis-
sion, and visible, infrared or radar scattering, is done using computer
programs whose input data are specific to the phenomenon being studied,
and use the results obtained with the flow programs described in Section 4.1.
4.2. 1. Calculation of radar attenuation
Absorption is the major cause of radar attenuation. On the line-of-sight of
the radar link that intercepts the plume, the attenuation is the sum of the local
discrete values of absorption expressed in decibels/cm according to:
a = 0, 08686
l -¥A /c-^’GT
1/2
where A = co 2 /(<9 2 + co 2 ) and co 2 = 3.181 x 10 3 n c (rad/s) 2
co, ,9, cOp and n c representing, respectively, the signal frequency, collision
frequency, plasma frequency and local electronic concentration of the plasma
environment. The signal frequency data are supplied by the missile designer;
the other data are obtained by calculations of the plume flowfield, using the
computer programs in Section 4.1.1.
Refraction, diffraction, and scattering are phenomena that are often
neglected, but may be very important in operational situations with high
electron concentrations in the plume. The effect of diffraction is to change the
polar distribution of radar energy in the far field of the plume. The result is
that the maximum attenuation (signal loss) value may be much less than
would be caused by line-of-sight absorption alone [5,13]. Refraction and
diffraction by the plume may also cause guidance errors by ducting around
the plume radar energy to and from the target, with a resulting shift in the
apparent target location.
Another radar interference effect is manifested as noise on the radar carrier
frequency, presumably due to scattering of the radar wave by large refractive
index gradients associated with high-velocity turbulent eddies in the plume.
This noise can interfere with and mask missile control information coded into
the radar wave [14-16]. The same scattering phenomenon causes backscatter
of the radar wave, manifested as the plume radar cross-section.
4.2.2. Calculation of optical transmission
According to the Beer-Lambert law, the transmission factor is expressed by:
T = e
-(No a + N<j d )Z
Plume, Signal Interference and Plume Signature
207
with
(7 a = -% and (7 d =
TIT n
Qd
nrl
N, r 0 , cr a , cr d are, respectively, the number of particles in the environment,
their average radius, the effective absorption and scattering cross-section, and
Z, the thickness of the medium traversed.
Q a and Q d are complex functions that provide the values of the absorption
and scattering coefficients, as a function of the optical refractive index n of the
particles, their radius, and the wavelength lambda of the signal. Electron
microscope measurements of the diameter of particles from samples taken
from the plumes and smoke trails of motors with variable flow rates resulted
in particle sizes ranging from 1/100 /mi to several tens of /mi.
The theory of scattering of light [17,18], enables us to calculate the various
Q d for each of the following three cases:
(1) where the radius of the particle is small in comparison with the
wavelength (Rayleigh scattering);
(2) where the radius of the particle and the wavelength are similar (Mie
theory);
(3) where the radius of the particles is very large in comparison with the
wavelength (the domain of geometrical optics).
Because the calculations in the Mie range are complex, a computer
program [19] is used to obtain the Q a and Q d coefficients for a population of
particles (in this reference, obeying a log-normal law of particle size distribu-
tion). The last calculation to determine the light intensity scattered in all
directions 6 by this cloud of particles is done according to:
, _ M 2 (/ 1 +/ 2 )
9 8 rln 2
with
/, =
rcr n
Qd p i
Pi = the function values tabulated by Deirmendjian [20].
The calculations of the coefficients of transmission through primary
smokes, based on experimental data on the nature and the size of the particles
ejected by the nozzle, provide a certain amount of useful guidelines for the
design of rocket propulsion propellants:
• Carbon soots are highly absorbing, regardless of the wavelength.
• As a rule, as long as the radius of the particles is not too great,
transmission in infrared is usually better than transmission in the visible
range.
208 Gerard Prigent
• The scattering indices of copper and carbon are fairly similar. Both are
high in terms of the signature of the plumes and smoke trails. Figure 8
shows, based on the size of the particles ejected by the nozzle, the
maximum mass fraction for a number of materials that cannot be
exceeded in order to keep a transmission through a given smoke trail (1 m
thick, 5 x 10~ 2 dilution) equal to at least 95%.
We observe that only a very small amount of carbon is required to degrade
the transmission in infrared at 10.6 /mi, and that zirconium oxide is found to
be better than aluminum oxide in the visible range.
4.2.3 . Calculation of infrared emission
The first models for infrared emissions in plumes appeared in 1967, in the
work of Rochelle [21]. They were followed by the NASA models and
Lockheed in 1973, Aerodyne in 1974, and finally Grumman in 1976 [22]. In
Fig. 5.8. Influence of the type, density and the radius of the particles, on the
infrared transmission at 10.6 jim.
209
Plume, Signal Interference and Plume Signature
1978 the JANNAF Exhaust Plume Technology Subcommittee undertook to
develop a standard model that included a standard plume flow model (SPF),
and a standard infrared radiation model (SIRRM) [23].
A typical simple model calculates the infrared radiation of a gas particle
mixture containing the main gaseous products (H 2 0, C0 2 , CO, HC1) and
one condensed species, alumina.
Results from calculations of the infrared radiation in the plume of a motor
burning aluminized propellant show that the infrared radiation is highest in
the afterburning region, and in its absence it is highest just behind the first
Mach disk.
4.3. PREDICTION MODEL FOR THE OCCURRENCE OF
SECONDARY SMOKE
Under specific temperature and humidity conditions, atmospheric water
vapor may condense into pure water drops and create fog. The combustion of
a propellant containing ammonium perchlorate leads to the mixing of
hydrochloric acid and water vapors. At a given temperature, and in the
presence of an azeotrope, the saturating vapor pressure of the mixture is
lower than that of pure water. This phenomenon results in condensation and
the formation of a secondary smoke trail in the operational range when such
propellants are used [24,25].
For a given temperature and humidity level, the quantity of condensed
water versus the dilution ratio of the combustion products in the air can be
determined. The mixing of these two vapors is assumed to be homogeneous,
without any chemical reaction, and its enthalpy assumed equal to the sum of
their total enthalpies. The conditions of thermodynamic equilbrium liquid/
vapor are calculated from tabulated experimental data. Two possibilities
emerge:
• the results of the calculations indicate that a complete lack of condensa-
tion is expected regardless of the dilution ratio of the combustion
products in the air: secondary smoke will never occur;
• the results of the calculations indicate that there is a dilution ratio for
which condensation is possible: this means there is a possibility that
secondary smoke will form.
The results are plotted for each propellant, in a curve of the type shown on
Fig. 2, that provides the minimum humidity level versus the ambient
temperature of the air above which secondary smoke may occur.
5. Influence of Propellant Formulation on
Transparency and Low Signature
At the start of a new program for a tactical or strategic missile, based on the
requirements of the missile manufacturer for transmission on through the
210
Gerard Prigent
plume and low plume or trail signature, the propellant designer is often led to
make a selection of the various ingredients that can be part of the formula-
tion.
5.1. FLASH SUPPRESSORS
The addition of potassium salts in the formulation of homogeneous EDB
and CDB propellants and Nitramites with high energy binder and HMX or
RDX makes it possible to suppress the afterburning. Because these additives,
for the most part, generate primary smoke, their percentage in the so-called
smokeless propellants, as described in Table 3, must be limited to the exact
amount required.
5.2. PARAMETERS AFFECTING THE RADAR TRANSMISSION
In composite propellants the K (potassium) equivalent content (K equiva-
lent % ppm of K 4- ppm x 1/10 of Na) is usually between 15 and 300 ppm. In
homogeneous or Nitramite propellants, containing no ballistic additives, the
level is often between 5 and 30 ppm.
Potassium in composite propellants is an impurity contained in the
ammonium perchlorate, and in homogeneous or Nitramite propellants, an
impurity contained in the nitrocellulose.
The K content of some insulation materials may reach 5000 ppm.
When there is afterburning in the plume, these amounts may cause very
Table 3 Classification of the propellants f based on their signature
Class
Primary
smoke
Secondary
smoke
Restrictions place on
the formulation
Smokeless
Very little
None
No aluminum
No AP
Very low level of
condensable species
Minimal smoke
Very little
Low density and
not frequent
Little or no aluminum,
Little AP(< 20%)
Very low level of
condensables species
Reduced smoke
Little
Yes
AP permitted
Very low level of
condensable species
High signature
Yes
Yes
None
a This classification cannot yet be considered as an international classification.
A working group of NATO/AGARD is now trying to define a standard international
classification.
211
Plume, Signal Interference and Plume Signature
high levels of transverse attenuation (see Table 4) and unacceptably high
signal loss in flight.
Other specific additives included in composite propellants exhibit anti-
attenuation characteristics (tin, chromium or lead molybdenum). The me-
chanism of their action in the plumes remains, for the time being, rather
poorly defined. It is thought, however, that they have the power to inhibit the
occurrence of the OH radicals that initiate the afterburning.
5.3. PARAMETERS AFFECTING THE PRIMARY SMOKE
Propellant metal fillers included as fuels, ballistic burning rate modifiers,
and the metal fillers of the insulation materials included as additives to
improve their heat resistance and structural integrity, are the main sources of
primary smoke.
Consequently, a compromise must be sought between the increased plume
signature and the gain in impulse due, for example, to aluminum.
Tests with a smoke meter show that the transmission in the visible range
through smoke produced by an 82% ammonium perchlorate Butalane drops
from 80% to 11% when the percentage of aluminum is from 0.5% to 8%
(rocket motor flow rate around 500 g/s).
The same type of measurements performed at X = 2 fim give two corre-
sponding transmission values of 95% and 30%.
Aluminum-free propellants, in spite of the possible presence of ballistic
additives, usually exhibit a very high level of transmission in the visible and
infrared ranges. To avoid degrading these qualities it becomes necessary to
optimize the nature and content of anti-instability additives included in the
formulation, particularly in the case of radial burning, and to use an inhibitor
producing little smoke for an end-burning propellant grain. In the last case,
even when the best inhibitors are selected, the transmission drops by several
percent. It is further necessary to optimize the igniter and the various rocket
motor materials that come into contact with the combustion gases.
Table 4 Transverse attenuation in a plume ; function of the ratio of alkaline impurities
Propellant
K Equivalent
ppm
Afterburning
Attenuation
dB
Frequency
GHz
CDB
21
yes
16
10
Nitramite 1905
(minimum smoke CMDB)
150
yes
16
16
Nitramite 1903
(minimum smoke CMDB)
3720
no
0.2
16
EDB
2635
yes
11
16
Butalite
(HTPB/AP)
45
no
1
10
212 Gerard Prigent
5.4. PARAMETERS AFFECTING SECONDARY SMOKE
To obtain a total suppression of secondary smoke, on the ground and in a
temperate climate, halogen, and therefore perchlorate, must be left com-
pletely out of the propellant. A very significant reduction in the frequency of
occurrence and the opacity of the secondary smoke can be obtained— in
Butalites— by limiting the proportion to less than 20%, as is the case for
Nitramites G (see Section 2.4, above).
Bibliography
1. Carpentier, R., Le Guidage des missiles tactiques. Bilan et evolution pour les annees 90.
Armement No. 84, 16-38, 1985.
2. Ramsay, D. A., The evolution of radar guidance. GEC J. Res., 3(2), 92-103, 1985.
3. Jarman, R. T. and Turville, C. M., The visibility and length of chimney plumes. Atmos.
Environ. 3, 257-280, 1969.
4. Jensen, D. E., Prediction of soot formation rates: a new approach. Proc. Roy . Soc. London,
Series A, 338-375-396, 1974.
5. Victor, A. C., Plume signal interference. Part 1, Radar attenuation. NWC China Lake.
California. NWC TP 5319 Part 1, 1975.
6. Mikatarian, R. R., Kaw, C. J. and Pergament, H. S. Air Force Rocket Propulsion
Laboratory. A fast computer program for non-equilibrium rocket plume predictions.
Aerochem Research Laboratories AD 751984 Aerochem-TP-282; AFRPL-TR-72-94. Au-
gust 1972.
7. Jensen, D. E. and Jones, G. A., Reaction rates coefficients for flame calculations. Combust.
Flame, 32, 1-34, 1978.
8. Prigent, G. and Dervaux, M., Prediction de l’attenuation electromagnetique de propergols
solides composites. Processus de combustion et de detonation. ICT Internationale Jahresta-
gung, Karlsruhe, 713-728, June 1979.
9. Dash, S. M., Analysis of exhaust plumes and their interaction with missile airframes.
Tactical Missile Aerodynamics. Progress in Astronautics and Aeronautics, Vol. 106, AIAA,
New York. 1986.
10. Mace, A. C. H., Exhaust signature predictions for rocket motors. AGARD Conference
Proceedings No. 391 (Confidential) Smokeless Propellants, 1985.
11. Ajdari, E., Methodologies et moyen d etude de la discretion des moteurs a propergols
solides. AGARD Conference Proceedings No. 391 (Confidential). Smokeless Propellants,
1985.
12. Victor, A. C. and Breil, S. H., A simple method for predicting rocket exhaust smoke
visibility. Spacecraft J. Rockets, 14(9), 526-533, 1977.
13. Senol, A. J. and Romine, G. L., Three-dimensional refraction/diffraction of electromagnetic
waves through rocket exhaust plumes. Spacecraft J. Rockets, 23(1), 39-46. 1986.
14. Victor, A. C., Plume signal interference. Part 2, Plume-induced noise. NWC, China Lake,
California. NWC TP 5319 Part 2, 1972.
15. Williams H., Wilson A. S., and Blake C. C. Scattering from a Turbulent Rocket-Exhaust
Jet Illuminated by a Plane Wave. Electron. Lett., 7(19), 595-597, 1971.
16. Clarricoats, P., Seng, L. M., Travers B. and Williams, H., Scattering from a turbulent
rocket-exhaust jet illuminated by a focused microwave beam, ibid, pp 597-600.
17. Kerker, M., The Scattering of Light and Other Electromagnetic Radiation. Academic Press,
New York, 1969.
18. Van Der Hulst., Light Scattering by Small Particles. John Wiley and Sons, New York, 1967.
19. Grehan, G., Gouesbet, G. and Rabasse, C., The computer program SUPERMIDI for
Lorenz MIE theory and the research of one to one relationship for particule sizing. ISL-R-
117,1980.
20. Deirmendjian, D. Electromagnetic Scattering on Spherical Poly dispersions. American Else-
vier, New York, 1969.
Plume, Signal Interference and Plume Signature
213
21. Rochelle, W. C., Review of thermal radiation from liquid and solid propellant rocket
exhaust. N.67.31300. NASA-TM. 53579, 1967.
22. Vanderbilt, D. and Slack, M., A model for emission and scattering of infrared radiation
from homogeneous combustion gases and particles. Grumman Research, AD-A027 576/8.
Department Memorandum RM-621, 1976.
23. Ludwig, C. B., Malkmus, W., Walker, J., Slack, M. and Reed, R., The Standard Infrared
Radiation Model A-81 -039063. American Institute of Aeronautics and Astronautics, Ther-
mophysics Conference. (U.S.), Vol. 16, pp 81-1051, 1981.
24. Miller, E., Smokeless propellants. Fundamentals of Solid Propellant Combustion. Progress
in Astronautics and Aeronautics, Vol. 90, AIAA, New York, 1984.
25. Victor, A. C., Computer codes for predicting the formation of rocket exhaust secondary
smoke in free jets and smoke chambers. NWC, China Lake, California. NWC TM 3361,
1978.
CHAPTER 6
Structural Analysis of
Propellant Grains
BERNARD GONDOUIN
1. Introduction
Causes of operational failures of solid rocket motors are varied, but the
major causes are tied to the structural integrity of the propellants. During
their entire service life propellants are subjected to stresses which, in some
cases, cause cracks in the propellant grain or separation between the
propellant and the inhibitor or the liner. During firing, there are a large
number of possible consequences from one of these structural failures.
1.1. PROPELLANT STRUCTURAL FAILURE
A crack in the propellant grain results in additional burning surface. The
increase in pressure resulting from this accidental increase of the burning
surface may lead to either the destruction of the motor, if the pressure is
greater than the burst pressure of the motor case, or operation outside of the
specifications (modification of the thrust, the burning time, etc.).
1.2. BONDING SEPARATION
A bondline separation, when it results in an increase of the burning surface,
triggers the same occurrences as described above. Another type of failure may
occur, however. The bonding of the propellant with the other materials
(inhibitor or thermal protection) is usually located somewhere close to the
wall of the case; burning in the debonded area may cause a significant heating
for the structure with a risk of burnthrough that would result in an abnormal,
and possibly catastrophic, operation of the rocket motor.
215
216 Bernard Gondouin
There are two very distinct stages in the operational life of a propellant
grain:
• the stage before firing: this includes manufacturing followed by various
transportation and storage phases. The duration of this stage varies, and
could last from a few months to several years.
• the firing, which lasts from a few milliseconds to several seconds,
depending on the function expected from the motor.
The mechanical design problem that needs to be solved is the assessment of
the risk of a structural failure occurring in the propellant grain and that of
debonding during the two stages mentioned above.
An initial method of handling this problem would consist in taking a
number of samples during the manufacture of the propellant grains and
performing a variety of tests under well-defined conditions. This experimental
method requires a large number of tests. It can be contemplated for small
objects, with short and easy-to-implement operational conditions. In the case
of propellant grains for rocket motors, where dimensions can be quite large
and operational conditions difficult to reproduce, a large number of tests are
not feasible.
An analytical method allowing the determination, a priori , of the structural
integrity of the propellant grains seems better indicated. The principle is
simple, and consists of determining two values for each loading condition
(corresponding to the various phases of the service life). These values are the
induced stress or strain resulting from induced loads in the propellant grains,
and the allowable stress or strain.
In general, the induced stress or strain in a propellant grain is the
maximum stress or strain developed in the propellant. It is found at the
location where the propellant is the most mechanically constrained, known
as the “critical point.” The assumption is as follows: the level of stress/strain
at points surrounding the critical point does not influence the structural
failure risk of the propellant.
The location of the critical point and corresponding stress and strain are
generally determined using a numerical method (finite element method).
The “capability” or allowable stress or strain is the structural stress or
strain that must be induced in a propellant grain to cause a structural failure.
This value is determined through tests; it is a function of the stress and/or
strain measured at the point of structural failure of the test specimens during
the various mechanical properties tests performed on the propellant.
The ratio of the capability versus the load gives the factor of safety:
K C w'th K > * no structura l failure
S K < 1 structural failure
where:
C = capability of the propellant;
S = induced stress or strain in propellant grain.
Structural Analysis of Propellant Grains
217
If C and S have exact values, this factor must always be greater than 1 to
ensure proper mechanical performance of the rocket motor. The variable
nature of physical phenomena involved requires a probabilistic approach.
The probability of the capability being greater than the induced stress/strain
is assessed: it is the structural reliability F :
F = Pb(K > 1) = Pb(C > S)
The analytical method used for this purpose is discussed in this chapter. An
overview is provided in Fig. 1. The following questions will be addressed:
• description of the mechanical loads found in propellant grains;
• mechanical properties of the bonding;
• determination of the stress/strain in propellant grains;
• determination of the grain structural integrity.
Note: When assessing the grain structural integrity, another value is some-
times determined: the margin of safety, MS. It is written as follows:
C- S
MS = — — = K - 1
Fig. 6.1. Determination of the structural integrity.
218
Bernard Gondouin
Therefore, the reliability is the probability that the margip of safety is greater
than zero:
F = Pb ( MS > 0)
2. Description of the Mechanical Loads
The service life of a propellant grain before firing consists of a succession of
transport and storage phases, under conditions that are contingent upon the
mission of the missile.
The transport of a space missile to the launching site, for example, happens
only once. The propellant is subject to low magnitudes of vibrations, and the
temperature variations are often controlled.
Repeated transports of tactical missiles stored or carried beneath an
aircraft subject the propellant grain to major accelerations, vibration, and
temperature variations. Furthermore, storage of all rocket motors causes
creeping due to the effect of the gravity; and because of repeated and various
handling, the risks of falls or shocks are certainly not negligible. Lastly, at the
time of firing, the pressure rise in the combustion chamber and the accelera-
tion resulting from the induced thrust impose loads on the propellant grain,
in addition to those already induced during the pre-firing phase.
To analyze the effect of these various environments on the stress/strain
imposed on the propellant, it is necessary to make a distinction between the
two major families of propellant grains:
• case-bonded grains;
• free-standing or cartridge-loaded grains.
2.1. CASE BONDED GRAINS
2. 1. 1. Temperature changes
At the time of its manufacture the propellant grain is cast in the insulated
case. The propellant hardens and bonds with the case or its thermal
protection with the help of a liner at a temperature which is typically greater
than 40°C, known as the cure temperature. Following the curing phase the
propellant, subjected to temperatures that are lower than the curing tempera-
ture, induces a change in its volume. This change is bound to induce stress/
strain in the propellant because it is bonded to a rigid structure with a lower
thermal expansion coefficient. A field of thermal stress occurs. The sketches in
Fig. 2 illustrate this phenomenon on a cylindrical propellant grain.
In addition to the thermal stresses caused by temperature changes evenly
throughout the propellant grain, there are the stresses from thermal gradients
occurring during transient phases. These stresses play a greater role in the
propellant grain contained in tactical missile motors, where the temperature
changes are sometimes very quick.
Structural Analysis of Propellant Grains
219
Motor case
Propellant
- Curing Temperature T c
— Dimensions of the propellant cylinder:
Outside diameter 0 e
Inside diameter 0,
Length 1
b
The propellant is not bonded to the case
Storage temperature T s < T c
Dimensions of the propellant cylinder:
Outside diameter: 0 e = 0 e [1 + a (T s - T c )] < 0 e
Inside diameter: 0\ = 0, {1 + a (T s - T c )] < 0,
Length: l’ = l[1 + a (T s - T c ) ] < L
a Ratio of linear thermal expansion of the propellant
The propellant is bonded to the case
The structure sustains no deformation
Storage temperature T s < T c
The propellant cylinder sustains deformations
Dimensions of the resulting geometry:
Outside diameter: 0" e = 0 e
Inside diameter 0 ', max > 0,
Length/outside diameter L" e = L
Length/inside diameter l" < L
Fig. 6.2. Diagram of the effect of thermal shrinkage.
2 . 1.2 . Force of gravity
Long-term storage of a case-bonded propellant grain brings on a creeping
of the propellant grain due to the force of gravity. The motor case is usually
sufficiently rigid to keep its original shape. The strains observed on a
cylindrical case-bonded grain due to the effect of gravity are illustrated in
Fig. 3.
220
Bernard Gondouin
Initial geometry, without gravity
(and no thermally-induced deformation)
Vertical storage
(no thermally-induced deformation)
Fig. 6.3. Diagram of the effects of gravity.
2. 1.3. Pressure rise at firing
When a case-bonded propellant grain is fired, the pressure in the combus-
tion chamber increases within a few milliseconds to reach maximum operat-
ing pressure. Through the entire time the pressure is transmitted through the
propellant to the motor case. The deformation of the case induces a strain
field in the propellant and stresses at the bondline.
The strains occurring in a cylindrical propellant grain at the time of
pressure rise in the combustion chamber are shown in Fig. 4.
The combustion chamber pressure, at the time of firing, is not steady.
There may be significant variations, resulting in a deformation of the
combustion chamber, and as result all of the propellant grain faces are
subjected to different pressures.
Finally, eventual combustion instabilities may trigger a vibration state in
the propellant grain.
2.1.4. Curing under pressure
In Section 2.1.1 the effects of temperature changes on a case-bonded grain
are described. In a case where, during its entire service life, a motor is stored
after curing under controlled temperature conditions, the only thermal loads
intervening are due to the difference between curing and storage tempera-
tures. If it were possible to compensate for the variation in geometry due to
the thermal shrinkage with an equivalent change of geometry, the thermally
induced strain would decrease: it is the principle of curing under pressure. A
cylindrical case-bonded grain cured under pressure is described in Fig. 5.
Structural Analysis of Propellant Grains
221
Zero pressure in the motor case
n
Pressure p
Without the case when the propellant cylinder is subjected to
internal pressure only, it has the tendency to sustain significant
deformations.
Pressure p
The propellant is bonded to the case and presses against it.
Pressure p
The propellant is not bonded to the case the pressure causes
deformations in the case The pressure is exerted on all surfaces of
the propellant cylinder which sustains no deformation if it is
incompressible.
Fig. 6.4. Diagram of the pressure rise induced by firing.
Because in modern motor cases the deformations are small in the cylindri-
cal part, the pressures that should be induced to compensate completely for
the thermal shrinkage would simply be too great. Nevertheless, even a partial
compensation for the thermal shrinkage permits a reduction of the stresses
along the bondline and a decrease in the damage to the propellant grain
before its firing.
222
Bernard Gondouin
If A V(p c ) = A V the deformations in the propellant cylinder are zero
Fig. 6.5. Diagram of the principle of curing under pressure.
2.2. FREE-STANDING GRAINS
The major differences between the mechanical loads induced in case-
bonded grains and free-standing grains occur during propellant temperature
changes and pressure rises at firing. Theoretically there should not be any
stress/strain in a free-standing grain under thermal and pressurization loads.
(Figs 2b and 4d). In fact, there are transient phases for these two types of
loading conditions that eventually could create significant stress/strain.
Structural Analysis of Propellant Grains 223
2.2 . 1. Temperature changes
When a change in temperature occurs that is even throughout the
propellant grain, a free-standing grain deforms freely, and no strain results.
This is the case illustrated in Fig. 2b.
In transient phases, during which the temperature is different in each point
of the propellant grain, thermal stress/strain is created. In any type of thermal
cycle these thermal stresses are non-existent at the initial and final stabilized
temperatures; they can be measured only during the cycle (Fig. 6).
The maximum stress/strain value of a cycle depends on the distribution of
the temperatures in the propellant. Consequently, this particular stress/strain
is a function of the thermal properties of the material (thermal conductivity of
the propellant), of the boundary thermal conditions (convective heat transfer,
radiating heat transfer), and of the geometry of the propellant grain.
2.2.2. Pressure rise at firing
In the steady phase at firing, if the pressure is applied on all faces of the
propellant, the resulting stresses/strains are those occurring when a motor
case is subjected to an even pressure: it is known as an isostatic state of the
stress/strain.
During the unsteady phase the pressure in the combustion chamber and
the pressure taking place in the gaps between the propellant grain and the
case may increase at a different rate. The grain is thus subjected to pressure
gradients causing stress/strain in the propellant. At least two different
possibilities have been observed.
Fig, 6.6. Effects of a temperature change in a free-standing grain.
224 Bernard Gondouin
(a) Regular pressure increase in the gaps
The maximum pressure gradient to which the propellant grain is subjected
depends on the manner in which the pressure increases in the gap. Figure 7
illustrates the pressure evolutions for a cylindrical propellant grain with a
central port.
The question then consists in determining whether the propellant grain can
withstand the evolution of the pressure difference A p(t).
(b) Oscillating pressurization in the gaps
The dimensions of the gaps and the nature of the gases may cause an
oscillating pressurization, such as illustrated in Fig. 8.
Hence, in addition to the problem of a propellant grain subjected to a
pressure gradient A p(t) = P c (t ) - P^t )— identical to case (a)— there is a
Fig. 6.7. Pressure rise induced by firing in a free-standing propellant.
Fig. 6.8. Oscillating pressure rise induced by firing in a free-standing grain.
Structural Analysis of Propellant Grains
225
dynamic coupling between the propellant grain and the gases in the gap. This
is a very complex problem to resolve because the dimensions of the gap
evolve continuously, modifying the pressure rise conditions. An initial
approach consists in making sure that a natural frequency of the grain does
not correspond to the oscillation frequency of the pressure in the gap.
The mechanical loads described in the preceding section are usually the
most significant factors in the structural design analysis. Yet, during the
service life of rocket motors, other stresses/strains may appear that influence
the structural integrity of the propellant grains. These include dynamic loads,
typically shocks. These mechanical stimuli are not included in this chapter.
The grain structural analysis allows the clear identification of the param-
eters necessary to determine the margin of safety. These are:
• the temperature of the propellant;
• the pressure in the combustion chamber;
• the loading rate;
• the loading time.
They are used to calculate the boundary conditions, the behavior laws, and
the capability of the materials.
3. Some Generalities and Definitions
3.1. STRESSES AND STRAINS
An object which is subject to mechanical loading (stresses or displacements
applied to the external surfaces) finds a new state of equilibrium after the
deformation has taken place. In each point M of this object, there is an
infinity of forces applied to the infinity of planes traversing this point (Fig.
9a).
In relation to a P l plane, on a dSi surface element, a dF t force is applied; in
relation to a P 2 plane, on a dS 2 surface element, a df 2 force is applied.
For each of the planes, the dF forces are the sum of a component dF n • n,
normal to the plane, and a component dF t -t, contained in the plane:
dF = dF n • n + dF t t
The stresses applied to each plane are defined by the following equations:
o
n
lim
dS~* o
dFn
ds ’
T =
lim
dS~+ 0
dF,
dS
Consequently, there is an infinity of stresses at each point of an object
subjected to mechanical loading. The stress state is defined by a matrix
composed of nine components expressed in a given perpendicular axis
system. We use the term “stress tensor.”
226
Bernard Gondouin
Fig. 6.9a. Description of forces in one point of a body at equilibrium.
Fig. 6.9b. Description of the tensor component at one point of a body in equilibrium.
Similarly, a strain tensor is defined for each point; if u l9 u 2 and u 3 are three
components in a reference system ( Ox u x 2 , x 3 ) of the displacement of the M
point, the nine strain components expressed in the reference system are
written:
1 f du, du.
Structural Analysis of Propellant Grains
227
3.2. BEHAVIOR LAW: THE NECESSARY COEFFICIENTS TO BE
DETERMINED
To know the behavior of a material is to determine the law relating the
stress tensor to the strain tensor when the material is subjected to mechanical
loading. For each point, there is a relation:
° ij = $ijkl * E kl
stress tensor = behavior * strain tensor.
In its general form the behavior of a material is rather complex; it has been
demonstrated, however, that in a material that is homogeneous, elastic and
isotropic, the definition of the behavior is limited to two coefficients, which
are:
• the Lame coefficients A, fi\
or
• Young’s modulus and Poisson’s ratio, E and v;
or
• the shear modulus and the bulk modulus, G and K.
For infinitesimal strains there are equations between these three pairs of
coefficients (Table 1).
Table 1
Function of
X and n E and v G and K
Lame’s coefficients X
Young’s modulus E
Poisson’s ratio v
Shear modulus G
Bulk modulus K
Ev
(1 + v)(l - 2v)
E
WTV)
H(3X + 2n)
X + n
X
2(X + J)
n
2
X + -n
E
2 (TTV)
E
3(1 -2v)
K -
G
9 KG
3 RTg
3 K -2 G
2(3 KTG)
228
Bernard Gondouin
One or the other of these pairs of coefficients can be used indifferently. In
any Cartesian coordinates (x u x 2 , x 3 ), the stress tensor and the strain tensor
at an M point are expressed by the following six components:
for the stress tensor (Fig. 9b):
G 22 j o- 33 , cr 12 = cr 21 ; cr 13 = cr 31 ; cr 23 = cr 32
for the strain tensor:
£ 1 1 5 £ 22j £ 33> £ 12 — £ 21> £ll ~ fi 31> £ 23 — £ 32
The equations between stress and strain are then written as:
with E and v:
fill =^( <T H - V ( G 22 + ^33))
£ 22 = ^(<*22 ~ V ( CT 11 + ^ 33 ))
£ 33 = ^(<*33 ~ + a 22 ))
_l+ v _ 1 + V _ 1 + V _
®12 r- °'l2; e 13 — ^ °'l3; £ 23 — v °23
with X and fi:
with
= 2 hsij + S^Xe
i and j vary from 1 to 3
( 1 )
( 2 )
e — £ 11 + £ 22 + £ 33
8
ij
0 i
i=J
the Kronecker symbol
with G and K :
Any condition of stress, expressed by one of the equations described above,
can be written as follows:
with
a ij = G h + ^ij a 1 and j var y from 1 to 3
( 3 )
= jOu + a 22 + <^ 33 )
Kronecker symbol
o is the mean stress or mean pressure
o\j are the deviatoric stresses.
Structural Analysis of Propellant Grains 229
In parallel, the strain can be written under the same form, i.e. the equation:
/ c e
8 ij = e u + 3
The stress-strain equations are therefore written as:
o'ij = IGe'ij 6 equations for the deviatoric components
( 4 )
a — Ke 1 equation for the isotropic component
The isotropic component represents the behavior of material subjected to a
uniform load. For example, an isotropic object subjected to hydrostatic
pressure shows a uniform strain. The deformation of the object is the same in
all directions, and there is no shear effect.
The equations for the deviatoric components represent the behavior in the
case of a non-uniform loading, where shear effects occur.
These two types of behavior involve different physical mechanisms. It is for
that particular reason that during the behavior analysis of propellants, as well
as for the stress/strain analysis in a propellant grain, this formulation is
sometimes called upon, even though Young’s modulus and Poisson’s ratio
are traditionally used.
General comment. The components of the stress tensors and strain tensors
are expressed within the coordinate system. It is obvious that an object
subjected to mechanical loading is in equilibrium with a stress and strain
state which is independent of the coordinate system by which the components
are expressed. The notion of a tensor invariant is used in this case. The first
three invariants of the stress tensor and of the strain tensor are S l9 S 2 and S 3
for the stress, and J l9 1 2 and J 3 for the strain.
Si = 0*11 + ^22 + ^33
^2 = c 7 U* c7 22 “ a 12 4" 0’22 (7 33 — ^23 + 0'33 (T 1 1 — C 13
S 3 = the determinant of the matrix of the stress tensor coefficients.
These values are independent of the coordinate system selected; only a
function of these values can be used to represent the stress or strain states of
an object.
3.3. TESTS DESIGNED TO DETERMINE THE COEFFICIENTS
All that is needed to know the behavior of a material is the determination,
through simple tests, of one of the three coefficient pairs described above. In
practice, relations (1) and (4) alone are used.
230 Bernard Gondouin
3.3 . 1. Determination of E and v
In the following example we assume a parallelepipedic object with one
dimension greater than the other two (Fig. 10).
When this object is subjected to a force F in the direction of its greatest
dimension (Ox : in Fig. 10), the stress and strain induced in the material are:
er n and e u in the Ox x direction
er 22 and e 22 in the Ox 2 direction
er 33 and e 33 in the Ox 3 direction.
The only measurable physical values are the force applied and the deforma-
tion of the object.
On a surface that is free to deform itself the stress is equal to zero. Since the
dimension of the object in the Ox 2 and Ox 3 directions is very small, the
following can be written: o 22 = o 33 = 0.
Calling A l u A / 2 , and A/ 3 the variations of the dimensions of the specimen,
the stress and strain are written as follows:
F
e
611 “ h
o
II
fS
b
AL
£22 = ~r
‘2
O
II
C-J
b
AL
e 33 =t~
*3
Equation (1) enables us to write:
£ 1 1 = £ (^l 1 ~ v ( cr 22 + G* 33 )) =
1 V(J 1 1
£ 22 = £ ( cr 22 “ Kg’ 1 1 + G’ 33 )) = — — = “ ve : !
£ 33 — — V£ U
E (Young’s modulus) is obtained directly from the equation:
£ 11 ^2^3 A/i
and similarly, Poisson’s ratio v is written:
£ 22 _ & l 2 ^ /i
£ U ^2
( 6 )
V =
( 7 )
Structural Analysis of Propellant Grains 231
F
°n ■ e n fT
x/ 3
Fig. 6.10. Uniaxial tensile test specimen.
This parallelepipedic object is a unidimensional specimen. Its dimensions
may vary. In Fig. 11 several unidimensional specimens used to analyze the
behavior of propellants are described.
Comment. When analyzing the results of tests performed on propellant
grains which show a great deal of deformation, the use of eqns (5) to predict
the stress and strain is no longer valid. Indeed, when the changes of the
dimensions of the specimen are no longer small compared to the initial
dimensions themselves, the assumption of infinitesimal deformation is no
longer valid. It becomes necessary to use a specially designed mechanical
model [22]. Using a model adapted to large-scale deformation is a very
complex task; it requires a coherence between the methods of analysis of the
tests and the methods of structural analysis. Among the many ways of
performing the test analysis, the most widely used is as follows:
If ! and £ ! ! are the stress and the strain determined according to eqns (5),
the corrected stress and strain are to be written as follows:
On = Ou(l + £u)
( 8 )
232
Bernard Gondouin
Fig. 6.11. Widely used uniaxial specimens.
3.3.2. Determination of K
The measurement of the bulk modulus is done simply by measuring the
variation in the volume of an object of any shape subjected to hydrostatic
pressure. Based on eqn (4):
<7 = Ke
Structural Analysis of Propellant Grains 233
for a material that exhibits little strain, e corresponds to the change in
volume.
a is equal to the pressure applied.
3.3.3. Determination of G
Knowing E, v and K makes it possible to calculate G using the relations
existing between the various coefficients. There are, however, specific speci-
mens with which the shear modulus G can be directly determined. These are
the torsional stress or shear specimens shown in Fig. 12.
Uniaxial specimens (Fig. 1 1) are widely used for a variety of tests (Fig. 13):
• tensile tests (induced displacements);
• relaxation tests (constant strain);
• creeping tests (constant stress load);
• combined tests: (a) loading-relaxation-loading (LRL); (b) loading-
unloading-loading (LUL)
Fig. 6.12.
234
Bernard Gondouin
Fig. 6.13. Description of the various types of tests.
These tests are performed under various:
• temperatures;
• pressures;
• loading rates for the tensile tests, and durations for the relaxation and
creeping tests.
235
Structural Analysis of Propellant Grains
3.4. VARIOUS TYPES OF BEHAVIORS OF THE MATERIALS
To determine the behavior law of a material, it is necessary to perform
combined tests, such as loading-relaxation-loading or loading-unloading-
loading types of tests. Tensile tests alone are not sufficient to draw conclu-
sions on the behavior type of a material. For example, the results of a tensile
test listed in Fig. 14 can be obtained from materials whose structural integrity
is different, which can only be discovered through combined tests (Fig. 15).
In solid mechanics there are only two types of behavior:
• elastic or elastoplastic, where the rate of loading and the duration play no
role;
• viscoelastic or viscoplastic, where the rate of loading and the duration
modify the response of the material.
The behavior, for each of these families, may be either linear or non-linear,
since linearity satisfies the rules of homogeneity and additivity.
Homogeneity
if e,j(t) -> aij(t) ( 9 )
then ke i} {t) -> ko^i)
where k is any constant.
Additivity
if elj(t) -> <r-/0
and if sf/t) -» a} ft)
then elj(t) + ef/t) -* o\ft) + a* ft)
To determine the response of a material under induced stress and strain, it
is desirable first to determine the structural behavior type (elastic, plastic,
viscoelastic, and linear or non-linear); and second to select the tests best
suited for the future applications of the material and for the measurement of
its mechanical coefficients.
Fig. 6.14. Result of a classic tensile test.
Structural Analysis of Propellant Grains 237
4. Structural Properties of Propellants and Their
Bonding
4.1. PHYSICAL DESCRIPTION OF PROPELLANT
4. 1. 1. Composite and composite modified
double-base propellants (Chapters 10 and 11)
Composite propellants consist of small-particle-size solids in a polymeric
matrix. The loading ratios are, typically, very high (sometimes greater than
70% of the volume). The bonding surfaces between the binder and the fillers
are very important. When relatively low rate structural loading is induced
(a < Is -1 ), there is failure of the bonding between some fillers and the binder,
or failure of the binder close to a solid particle. Vacuum holes are created, and
their size increases with the stress/strain. This phenomenon generates a
dissipation of energy resulting in a viscous behavior, at a macroscopic scale
to which is eventually added the viscous nature inherent to the binder.
When these vacuum holes reach a significant size (several microns) they act
as microfailures initiating small cracks in the binder, and causing failure of
the propellant grain.
These phenomena correspond to two clearly distinct phases (Fig. 16).
• Stress/strain of the bonding between the binder and the fillers. It is the
structural properties of the binder and of the bonding that govern the
mechanical behavior of the propellant. The total solids content, their
Fig. 6.16. Tensile test on a composite propellant.
238
Bernard Gondouin
shape, and particle size distribution influence the propellant behavior by
affecting the bonding properties.
• Growth of the microfailures ( vacuum holes). It is the tearing characteristics
of the binder, as well as the total solids content and their size distribution
which rule the structural behavior up to the failure of the propellant
grain.
The behavior type of these propellants is determined by performing the LRL
or LUL tests. The aspect of the curves obtained (Fig. 17) indicates a non-
linear viscoelastic behavior.
Comment. Some composite propellants have a perfectly elastic binder. Since
the fillers themselves are also elastic, their viscous structural behavior is due
solely to the dissipation of energy at the bonding level between the binder and
the solids.
Fig. 6.17. L.R.L. and L.U.L. tests on composite propellant.
Structural Analysis of Propellant Grains
239
4. 7.2. Double-base propellant grains
The double-base propellant grains are gels containing at least two main
ingredients: nitrocellulose and nitroglycerine. According to the various
manufacturing methods, there are two main families (Chapter 9):
• solventless double-base propellants (also called extruded double-base
propellant EDB);
• cast double-base propellants (CDB).
These are homogeneous propellants from the aspect of structural mechanical
properties; but their production process may cause anisotropies, for instance
in EDB propellants.
Their physical structure looks like a solid phase (nitrocellulose), consisting
of a continuous tridimensional network inside of which there is a liquid phase
(nitroglycerine).
Usually, this structure leads to materials which are more rigid than the
composite propellants, but when mechanical loading is imposed, the presence
of the two distinct phases causes energy dissipations resulting in a more or
less pronounced viscous behavior.
Comment. Crosslinked double-base propellants (Chapter 11) have some of
the characteristics of the double-base propellants: the binder has the physical
structure of a gel, which is crosslinked. They are, nevertheless, ranked as
composite propellants insofar as the solids content ratio is such that the
bonding phenomena between the binder and the solids are the predominant
factors and govern the behavior of the propellant.
4.2. MECHANICAL BEHAVIOR OF THE PROPELLANTS
Each type of propellant has its own specific mechanical characteristics.
Still, the methods used to determine their behavior are identical for every one
of them, and the influence of the various parameters (temperature, pressure,
loading rate) is the same overall for all propellants. Consequently, distinc-
tions will no longer be made between each type of propellant in the following
sections of this chapter.
4.2. 7. Tensile behavior
The tensile tests are widely used for the fine analysis of the propellants’
behavior as well as for the manufacturing controls of these propellants.
Because their behavior is not linear elastic, it is necessary to define a certain
number of parameters that allow a better representation of the aspects of the
experimental curves. These parameters, shown in Fig. 18, are:
E Young’s modulus, or tangent modulus, or initial modulus;
<r m maximum stress;
240
Bernard Gondouin
Fig. 6.18. The various parameters describing a typical curve.
e m strain at maximum stress;
e r strain at rupture.
The capability, as defined above in Section 1, for a tensile test is expressed by
the maximum stress <x m , and the strain £ m , or by any other function taking
these two parameters into consideration.
When the aspect of the tensile curve differs from the curve shown in Fig. 18,
other values need to be determined.
The values for the parameters defined above vary with each propellant
type, and with the pressure, temperature, and loading rate parameters for
each propellant. Age and humidity are also common factors which affect
these parameters.
When it is used in the case-bonded form, the propellant must exhibit the
greatest possible £ m during the thermal cycle and at the time of firing. On the
other hand, maximum stress, a m must be high for the stress induced by
acceleration (gravity and flight of the missile).
The problem is different in the case of a free-standing grain, and in fact this
type of configuration is selected for highly rigid propellants (high modulus £),
with high <r m and low £ m . For example, this is the case with double-base
propellants.
During a tensile test the physical nature of the propellant (described in
Section 4.1.) results in an increase of the volume of the specimen, caused by
the occurrence of vacuum holes around some crystalline fillers, or by the
increase of micro-cracks in double-base propellants. Knowledge of these
phenomena contributes greatly to the determination of the behavior of the
materials.
The simultaneous measurement of the volume dilation during a tensile test
is done with a gas dilatometer developed by Farris [4]. The method consists
in measuring the pressure variation in an enclosure where the specimen is
Structural Analysis of Propellant Grains 241
placed. The change of the pressure is directly linked to the volume dilation of
the specimen.
The general aspect of the curves obtained is shown in Fig. 19.
Phases I, II and III of the behavior illustrated in Fig. 19 can be understood
in the following manner:
Phase I The zero relative volume dilatation corresponds to an incom-
pressible behavior.
Phase II Creation of vacuum holes or micro-cracks.
Phase III Size increase of the vacuum holes and micro-cracks.
The e d value is also called de wetting strain; it identifies the threshold above
which the propellant is no longer incompressible. For composite propellants,
the higher its value, the better the bonding between the binder and the
oxidizers will be. It is a characteristic indicative of good structural integrity of
the propellants. e d depends on temperature, loading rate, and pressure
imposed.
As a rule, e d increases with the temperature, or when the loading rate
decreases, or again when the pressure increases.
It is difficult to assign values to the dewetting elongation, since this
parameter may take different values for each propellant with the pressure ( p )
temperature (T) and loading rate (e) parameters. For composite propellants
with a 20°C temperature, at atmospheric pressure, and a e loading rate of the
order of 10“ 2 s -1 , e d is usually comprised between 7 and 12%.
a, the angle formed by the asymptote with the axis of the strains,
corresponds to the quantity of vacuum holes or micro-cracks present in the
propellant. The smaller the number of cavities in the propellant, the smaller
tgot is (a favorable characteristic). As in the case of e d , tgoa varies with the three
p, T , and e parameters. As a rule, tga decreases when the pressure increases,
when the temperature increases or when the loading rate decreases.
A V/V 0
e
I II III
Fig. 6.19. The three behavior phases of a propellant. During a tensile test with
measurement of the volume dilatation.
242
Bernard Gondouin
In composite propellants tga must be as low as possible, but the selection of
the propellants must be primarily based on a dewetting strain that is as high
as possible.
A particularly interesting test, which is derived from the tensile test,
consists in varying the temperature of the propellant specimen during a low-
speed tensile test. This test corresponds to the stress imposed on the
propellant in a case-bonded propellant subjected to a temperature drop.
The stress response is illustrated in Fig. 20.
Given T f as the temperature at rupture of the specimen; the elongation at
break obtained during a tensile test with simultaneous cooling is much higher
than for a tensile test performed at a constant T f temperature and identical
loading rate.
Fig. 6.20. Tensile test with simultaneous cooling of the specimen.
Structural Analysis of Propellant Grains
243
Results of tests performed with propellants under various testing condi-
tions are given in the table and diagram in Fig. 21. Of great interest is the fact
that when a case-bonded propellant is cooled down, the e m elongation
capability depends on the way the cooling-down is handled. Figure 21 shows
the evolution of this parameter as a function of the ratio of the loading rate to
the cooling-down rates. For a given propellant, subjected to a cool-down,
there is a corresponding value of the Ae/AT, and a maximum allowable
elongation value corresponds to that ratio.
4.2.2 . Stress relaxation and creep
The viscous nature of the mechanical behavior of a propellant is demon-
strated by relaxation and creep tests.
The relaxation test, which consists in subjecting a specimen to a constant
elongation and in measuring the evolution of the stress, corresponds to the
mechanical load existing in a case-bonded propellant stored at a constant
temperature, below the curing temperature.
T in °C/h
V T in
mm/ min
T,
°C
E m in %
o m in MPa
'!?' %/ ’ c
-10
0,05
-72
55
13,5
0,6
-10
0,1
-67,5
105
6,3
1,2
-5
0,05
-70,8
109
7,8
1,2
-20
0,1
-70
54
9
0,6
-7
0,1
-65,8
147
4,5
1,71
T = - 60°C
0,1
11,4
12
isothermal
tensile test
150
c
£
100
50
I A t /AT
J I
1 2
%/• c
Fig. 6.21. Results of tensile test with simultaneous cooling.
244
Bernard Gondouin
The creep test consists of subjecting a specimen to a constant load and in
measuring the evolution of the elongation. This test corresponds to the
mechanical loading induced into propellants subjected to a constant acceler-
ation.
(a) Relaxation
In a relaxation test performed on an uniaxial specimen, if e t is the constant
elongation prescribed during the test, and if o (t) is the evolution of the stress
versus time which is measured, the relaxation modulus E R (t) is expressed by:
£r(0 =
g(0
Similarly, in a creeping test, the compliance J(t) is expressed by:
( 11 )
( 12 )
The compliance is the inverse of a modulus.
The shape of the relaxation modulus E R (t) looks like the illustration in
Fig. 22.
For the propellants, the relaxation modulus usually depends on the
temperature and the strain level. For an identical amount of time, the
relaxation modulus decreases when the temperature increases, or when the
strain level increases (Fig. 23).
When the variation in the relaxation modulus versus the strain level is
small, a linear viscoelastic law can be used. At a given temperature, the curve
plotted on Fig. 22 can be written using one of the following forms:
Homographic form
E R (t) = E x +
log E (10 5 Pa) logE(10 6 Pa)
Structural Analysis of Propellant Grains
Effects of the Strain Level
245
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
Effects of the temperature
o
>
■
A
A
o
>
■
A
A
o
t>
■
0
Temperature
o -50°C
t> -4CTC
■ -3CTC
a 2CTC
a 6CTC
log time (min)
Relaxation Strain 10%
A
.Aj
3
Fig. 6.23. Effects of the temperature and of the level of elongation on the relaxation
modulus.
246 Bernard Gondouin
E u E 2 , t and n are characteristic constants of the material that are
determined experimentally.
Prony series
E R (t) = E 0 + £ Etc' 1 * (14)
i= 1
£ 0 , E t and are characteristic constants of the material that are determined
experimentally.
When tests are performed on an uniaxial specimen, the stress is expressed
by the relation [2,3] :
ft
<7(t) = E R (t)e(o) + j E R (t - t) ^ di (15)
This form is valid only for a linear viscoelastic behavior.
In the case of non-linear behaviors, some authors propose using the same
form as (15) by expressing the relaxation modulus into the product of two
terms.
£ R (t,£) = £ R1 (£)£ R2 (0 (16)
E Rl (e) may take the form of a polynomial.
Other authors propose laws that are better suited to propellants [9];
Francis has done a comparison of the laws developed by various authors for
solid propellants [13]. No model appears completely satisfactory, and major
research work is still being done in this area [23].
(b) Creeping
The creep test is used only to determine the failure characteristics of solid
propellants. A constant load <r F is applied on a specimen; the time to failure t R
is recorded (Fig. 24).
4.2.3 . The effect of the temperature;
time-temperature equivalence
When relaxation tests are performed (at a given elongation) at various
temperatures, the curves representing the evolution of the relaxation modulus
for each temperature are deducted one from the other by a shift factor versus
time (Fig. 25). This observation is generally true in the case of polymers.
There is an equivalence between time and temperature. In the case of the
relaxation, we can write:
£r(*o, T 0 ) — E R (t u 7]) — £ R (£ 2 , T 2 )
Structural Analysis of Propellant Grains 247
where:
log t l = log t 0 + log a£°
log t 2 = log t 0 + log a£°
where a£° and a^ are the shift factors, in relation to the T 0 reference
temperature.
A sole curve can be identified, called the “master curve,” which gives the
value of the relaxation modulus versus a reduced time t/a£° for various
temperatures. The corresponding time, called reduced time, is written as
follows:
Jo a r°(^X T ))
The shift function is determined experimentally. Williams, Landel and Ferry
[10] have developed an analytical form with two coefficients, and C 2 ,
usually known as W.L.F. equation:
log a£ 0 =
-c t (r- r 0 )
c 2 + t-t 0
The reference temperature T 0 is often the ambient temperature, and the
corresponding shift factor is written: a T .
248
DETERMINATION
OF Log a T T
Bernard Gondouin
PLOT OF THE
MASTER CURVE
log (t/Or)
Fig. 6.25. Time-temperature equivalence.
Extending the concept, the principle of time-temperature equivalence is
used on all characteristics measured experimentally during tensile tests:
• tangent modulus E;
• maximum stress a m ;
• strain at maximum stress e m .
In the case of tensile tests it is an equivalence loading rate (e) - temperature
that is used. The master curves are defined with the reduced variable l/ea r .
log E = /(log l/ea r )
l°i <7 m = 9 ( log l/ea r )
log e m = h ( log l/ea r )
249
Structural Analysis of Propellant Grains
Time to failure at maximum stress <r m is:
t m = eje
It becomes possible to plot the master curve under another form (Fig. 26).
log a m = g'(log tJ* T )
For some number of propellants, the shift factors measured on the moduli
and on the maximum stresses are identical.
The time-temperature equivalence concept is empirical. Consequently, it
must be determined for each propellant.
4.2.4. Effect of the pressure
It is necessary to know the effect of the pressure on the mechanical
behavior of propellants as well as on their capability because, at the time of
firing, the propellant grains operate under pressure. This pressure varies
according to the propellant grains from 4 MPa to 15 MPa, and possibly
higher.
Tests performed under pressure on specimens are done at constant
pressure; the strain imposed on the propellant in a case-bonded grain is
different, because the evolution of the stress and strain is due to the evolution
of the pressure. To obtain the best possible simulation of the firing phenome-
na, it would be necessary to perform tensile tests with simultaneous pressure
variation.
Qualitatively, during a tensile test, the effect of the pressure is to delay the
occurrence of micro-cracks and vacuum holes. The relative variation in the
Fig. 6.26. Master curve of the maximum tensile stress.
250
Bernard Gondouin
volume that is measured during the test reveals an increase in the dewetting
elongation and a decrease in tga.
The values of the maximum stress and corresponding strain are signifi-
cantly increased in comparison with the values obtained at atmospheric
pressure under the same temperature and strain rate conditions (Fig. 27,
upper). For any common incompressible portion where the relative volume
variation is zero, at atmospheric pressure and under pressure the propellant
behavior is, of course, unchanged.
In the case of composite propellants with large elongations, and with a
significant Phase III (shown in Fig. 19), the effect of pressure is generally
described as follows (Fig. 27, lower).
Phase I. The propellant is incompressible, the amount of vacuum holes
around the charges is low, possibly zero; the pressure has no effect on the
behavior, and the tensile curves are identical for all pressures.
Phase II (of a test performed at atmospheric pressure). The number of
vacuum holes increases and reaches maximum value at stress The effect of
the pressure is to delay the occurrence of the vacuum holes and to
significantly decrease their number. With pressures of the order of 7 MPa, the
number of vacuum holes stays very low until stress Stress and the
corresponding elongation must be compared to the strain at the end of
Phase II, (t x , and the corresponding elongation The tensile behavior of
highly filled composite propellants often exhibits only Phase I and II at
atmospheric pressure. As a result, the comparison between the maximum
stress and corresponding elongation presents no problem (Fig. 27, upper).
Phase III (of a test at atmospheric pressure). All vacuum holes have
appeared; their number remains constant until stress o m . Their size increases
between and e m and the difference between e m and e 1 is characteristic of the
resistance to tearing of the binder. Under pressure, this phase may completely
disappear. When micro-cracks appear in the binder, at a stress close to the
maximum stress , which is much greater than the corresponding stress at
atmospheric pressure (cTi), the propagation of the cracks in the binder is
much more rapid under pressure. Phase III is greatly reduced, sometimes
practically nonexistent. It is therefore important to compare the correspond-
ing stress and strain, respectively, because although the maximum stress of
tests performed under pressure is typically greater than any stress exper-
ienced under tests at atmospheric pressure (o^ > and cr^ > <x m ), it is not
true for elongations (e^ > and < e m ).
The following question needs to be answered: which capability is to be
taken into consideration? The effects described above increase when the
pressure increases, up to a threshold pressure, after which the effects remain
constant.
Structural Analysis of Propellant Grains
251
That threshold pressure depends on the materials, and for each propellant
it depends on the rate of stress and the temperature. In fact, the higher the
stiffness of the specimen, the greater the threshold pressure will be (Fig. 28).
4.2.5. Behavior law of solid propellants
Section 3.2 describes the coefficients that must be determined to know the
mechanical behavior of the propellants.
All of the tests described above reveal a non-linear viscoelastic behavior,
tricky to represent in a single model.
252
Bernard Gondouin
The first important result is obtained during the tensile test with the
simultaneous measurement of volume dilation. The volume dilation is zero
up to elongation e d , which corresponds to incompressible behavior of
propellants under small strains. Incompressibility, in the equations of me-
chanics, is a discontinuity which expresses itself by the fact that it is not
possible to determine stress field from the strain field. The average stress d
depends on the geometrical confinement of the propellant.
Returning to the definition of the coefficients characteristic of the behavior,
incompressibility is expressed by:
E (any) v -► 0.5
or G (any) K -► oo
In fact, the bulk modulus has a finite value, but it is much greater than the
shear modulus.
For that reason, relations (4) are used. In the case of a viscoelastic
behavior, the formulation becomes:
G'iM) = 2G(0fi}/ 0) + 2 P G(t - T)£' 0 <T)dt
Jo
<7 (t) = ke(t)
( 17 )
where:
o'ij(t) and e'ijit) are the deviatoric stress and strain tensors;
a(t) is the average stress;
e(0 = 3e(0;
e(0 is the average strain.
Structural Analysis of Propellant Grains
253
For infinitesimal strain, the volume dilatation is equal to e(t). For an
incompressible mechanical behavior, the relations between coefficients E, v
and G, K, become:
E = 3G; v = i (18)
Therefore, the relaxation modulus identified in Section 4.2.2 allows us to
calculate easily the G modulus, and the relation between the deviatoric
tensors will be established simply. The relation between the average stress
and the average strain is more complicated because, as a rule, e(t ) is very
small and K is very large. The methods used most widely to handle this
problem are described in Section 5.
Propellants generally have a non-linear viscoelastic behavior. The laws
used to model this type of behavior are mentioned in Section 4.2.2.
Starting with relation (17), which is valid for a linear behavior, an
extension can be done by writing:
a'ij(t) = 2 f G(s, t - T)e;/T)dT + 2 G(e, t) £ o<0) (19)
Jo
There have been other formulae proposed to model propellant behavior
[13]. Farris [4], in particular, developed a theory that applies to composite
propellants. This law is written:
Deviatoric stress tensor
AM) = exp{/?/y - m + G <^)>
+c (‘-(w;)1I <, - {r ^ ,d{ } (20)
o'ij = deviatoric stress tensor
By = deviatoric strain tensor
AV/V 0 = volume dilatation
if e x , e 2 , e 3 are the principal strains
ly = i(( £ l - £ l) 2 + ( £ 2 - £ 3) 2 + ( £ 3 “ £ l) 2 ) 1/2 Pyllp,
1/Pl
a T = shift factor of the time-temperature equivalence
f
— is the reduced time
II /y II 00 = max l ; yl
G lf G 2 , G 3 , P, P\ m u m 2 , m 3 , Pi
are constants that are dependent on the material.
Bernard Gondouin
254
Isotropic part
A, + A 2 (T - T 0 )
( 21 )
A V/V 0 = £ j^expj^! + Xi(T ~ To))' - lJJ
+ Aly exp j|”
d = (<7 U -f @22 + ^ 33 )/^ is the average stress;
K , A, r, Xu fa* A 2 are constants of the material.
In most cases this law can be simplified. It allows us to represent, with a
fairly good level of accuracy, the behavior of the propellant as a function of
various physical parameters: temperature, pressure, and strain rate (Figs
29-32).
EFFECT OF THE STRAIN RATE (20C)
• modeling
9.79 r
8
Cl „
w , 1
« 4F
0 r
co
/
/
• /•'
/
experiment
# — • 500 mm/min
— - , _
“*• 50 mm/min
— • • — 5 mm/min
A
y
10
20
Strain (%)
30
Fig. 6.29. Model of the Farris law behavior.
Structural Analysis of Propellant Grains
255
-30-C
■ Modeling
Experiment
Strain
Fig. 6.30. Influence of the temperature.
Some points of the field are modeled with a great lack of precision, which is
a serious disadvantage when used systematically. This remark seems to have
been justified for most of the models proposed by various authors [13].
In fact, the modeling of a behavior law can be done according to two
methods:
(a) Experimental results are written into models according to various
mathematical expressions (polynomials, power laws), which are not
necessarily supported physically. In this case the precision of the model
selected depends on the quantity of tests performed to explore the
experimental field.
(b) The choice of a constitutive law to approximate the behavior based
upon the modeling of the physical phenomena involved during the tests
(for example, with composite propellants, the dissipation of energy
256
Bernard Gondouin
- Modeling
experiment
strain
Fig. 6,31. Influence of pressure.
through the creation of vacuum holes, growth of cracks and ripping of
the binder until a break occurs). This method, based predominantly on
physics, and therefore more real, should allow us to obtain a global
modeling of the behavior of propellants, with a good level of accuracy
over a fairly extensive experimental field. In fact, the physical phenome-
na taken into consideration do not correspond to all physical phenome-
na involved. The simplified assumptions used to create the models do
not have the same degree of validity for the whole field examined. For
some conditions of utilization, some phenomena that have not been
taken into consideration may modify the behavior, and the modeling
used will be imprecise.
Structural Analysis of Propellant Grains
257
■ Modeling
Experiment
Strain
These slightly pessimistic comments do not prevent research activities from
continuing, which is a good thing. Even though it seems improbable that we
will be able in the short term to use a constitutive law expressing the complex
behavior of propellants, the development of modeling, even if it can never be
completed, increases considerably our knowledge of propellants and gives us
the possibility of improving their structural integrity.
4.2.6. Capability: failure criterion
4.2.6. 1. Capability (allowable stress or strain)
The propellant capability is the induced maximum stress or strain neces-
sary to cause failure of the material.
258
Bernard Gondouin
The propellant capability, under tensile load, may be expressed either by
the maximum stress a m , or by the corresponding maximum elongation. If
cracks appear at elongation e m and propagate throughout the specimen up to
e r (Fig. 18), the propellant cannot be used for an elongation ranging between
e m and e r .
The capability of a propellant is determined experimentally. It is expressed
by using master curves (Fig. 33).
log t/a, (t in min)
Fig. 6.33. Tensile master curves a m and e m .
Structural Analysis of Propellant Grains
259
4. 2. 6. 2. Failure criterion [ 14 ]
The propellant capability, as defined in Section 4.2.6. 1., corresponds to a
monodimensional test. The stress tensor is reduced to a single component.
CT m 0 0
5 — 0 0 0
.0 0 0 .
In a propellant grain the stress tensor has, at each point, more than one
non-zero component. Consequently, it is not possible to do a direct compar-
ison between the capability obtained by monodimensional tests and a three-
dimensional stress field.
When inducing a mechanical load, there is at each point of the propellant a
stress tensor and a strain tensor. These tensors can be characterized by their
three principal components and the corresponding invariants (as defined in
Section 3). The stress tensor (or strain tensor) for each point of the propellant
grain is represented by one point in the principal stress space (or principal
strain space). In that space there exists a volume where the propellant keeps
its structural integrity, where there is a little damage, and a volume where the
propellant is made worthless by significant damage, even possibly a crack. It
is sufficient to ensure that the points representative of the stress tensor in the
propellant are located in the volume where the propellant keeps its structural
integrity.
Generally, the propellant is considered worthless when it is ruptured. The
two areas are separated by an assumed continuous surface, called the failure
surface. It is defined only in stress, and it is obtained with different tensile tests
under different hydrostatic pressures, different temperatures, different tensile
rate, and biaxial and triaxial tests.
Several authors have proposed different equations for these surfaces [14].
For propellants in general, it seems that the best-suited equation corresponds
to a mixed formula:
• the Stassi formula for the area where the stresses are positive or slightly
negative;
• the Von Mises formula for the area where the stresses are negative
(Fig. 34).
These two formulae correspond to revolution surfaces centered on the axis A
where = o 2 = <r 3 . Figure 35 shows the intersection of that surface with a
plane containing the A axis. Axes A and Y of this new space are related to
values using invariants of the stress tensors:
A is the axis of the average stresses a oct = + o 1 + <r 3 ) Y is the axis of the
octahedral shear stress
T 0 c. = Hfal - + (Pi - ff 3> 2 + (<T 3 - ffl) 2 ] 1/2
260
Bernard Gondouin
Fig. 6.34. The failure criterion.
Fig. 6.35. The failure criterion shown in a two-dimensional axis system.
All points representative of the stresses in a propellant grain are located
within that plane. Taking a point M in this plane, the homothetic curve to the
curve @1 (representative of the failure surface) passing through M cuts the axis
er 3 /er m at a point whose measurement on this axis is o 0 is called the
equivalent stress. It allows us to compare directly the three-dimensional
stress state represented by the point M to the maximum stress obtained in a
tensile test.
Structural Analysis of Propellant Grains
261
For the Von-Mises part, this equivalent stress is defined by:
<7 0 = [[fal - <*2 ) 2 + (<7 2 - <7 3 ) 2 + (<7 3 ~ <7i) 2 ]/a] 1/2
and for the Stassi part :
<7 0 = [(<7l + <7 2 + <T 3 ) + {(<Ti + <7 2 + <T 3 ) 2
+ b[(<T i - <7 2 ) 2 + (CT 2 - <7 3 ) 2 + (<T 3 - <T!) 2 ]} 1/2 ]/c
a, b , and c are coefficients that depend on the material.
Comment. The use of this failure criterion implies that the effects of the
pressure observed on the stress capability are identical to the effects on the
strain capability. It is therefore necessary to verify, experimentally, that the
gain contributed by the pressure to the stress is at least equal to the gain
contributed to the corresponding strain.
Furthermore, if the failure surface of a propellant is not identical for all
stress rates and temperatures tested, the failure criterion defined in this
section does not exist. When this occurs, the propellant capability must be
determined experimentally under conditions similar to the operating condi-
tions (stress rate, temperature and pressure), using multiaxial specimens.
4.2.7. Damage
The capability defined in the preceding section corresponds to an elemen-
tary mechanical load, i.e. one rate of load, one temperature and one pressure.
Propellant grains are subjected to various loading conditions whose effects
are cumulative in time. It is therefore necessary to introduce the notion of
damage, which represents the ability of the material to be subjected to a
cumulation of various elementary loads.
Several models have been suggested. Currently, the most widely used
model for propellants is the Bills model, based on the Miner model, and
defined as follows: [4,23-25]
» = I r- (22)
i= 1 l Ri
where:
i represents the various elementary loads;
t t represents the time spent under elementary loads i ;
t Ri represents the failure time corresponding to the elementary load i;
2 is the damage which, by definition, must be less than 1 for
the propellant to be used.
When the creep failure curve is written in the form of:
262
where:
Bernard Gondouin
o F is the applied load in creeping;
t R is the failure time for applied load tr F ;
m and $) 0 are the coefficients depending on the material.
The damage can be expressed as follows:
rr dxl 1/m
m = &o J 0 (c7 oW) m - (24)
In this manner the entire history of the stress is taken into account,
regardless of the nature of the mechanical loads that are applied.
The creep failure curves cannot always be written in the form of eqn (23). In
that case, a more general form to express damage is:
9(t) = 9 odkoU^+^dkolU^ 3 (25)
9 09 @ 3 and m are constants of the material.
4.2.8. Tearing
Cracks may occur in the propellant as a result of certain manufacturing or
handling operations without necessarily compromising the operation of the
rocket motor.
To assess the severity of a crack it is necessary to determine the manner in
which it propagates itself under the effect of mechanical load.
There are three modes in which a crack propagates itself (Fig. 36).
A stress intensity factor at the tip of the crack is determined for each
propagation mode (X,, X„, X,„). It is typically dependent on the initial length
a 0 of the crack and on the stress that would exist in the area at the bottom of
the crack if the crack were not there. As a rule, the propagation rate of cracks
obeys a power law for the stress intensity factor.
Mode I Mode II Mode III
(tensile stress) (Shear stress) (Shear stress)
Fig. 6.36. The three modes of propagation of a crack.
In a propellant grain, when cracks exist, they propagate themselves primarily
in Mode I and II.
The tests designed to determine the propagation in Mode I are performed
on special specimens (biaxial notched strip specimen) which are subjected to
tensile stress in a direction perpendicular to the crack (Fig. 37).
During the test, the length of the crack does not evolve in a continuous
manner [26]. But, by proceeding to an integration of the phenomenon, it is
possible to obtain an average evolution of the propagation rate of the crack
(Fig. 38), as well as the intensity coefficient of the stress.
Crack propagation tests give results that are very scattered. The laws
describing the phenomenon can be only an approximation of that pheno-
menon.
Nonetheless, the law described below [15,16] permits a global representa-
tion of the crack propagation phenomenon in propellants (Fig. 39).
* - a *L.
Fig. 6.37. Notched biaxial strip specimen.
264
Bernard Gondouin
IT
MPa
t min
Fig. 6.38. Evolution of the length of a crack and of the stress during a test.
A material constant;
da
— propagation rate of the crack;
d t
o m tensile capability of the material for the corresponding
mechanical load (same tensile rate);
t m time to failure corresponding to tr m ;
Kj stress intensity factor in Mode I.
There are other authors proposing laws for viscoelastic materials [17-19]. A
significant amount of research is being done currently in this area; crack
modeling in solid propellant grains continues to be done with simple models.
Structural Analysis of Propellant Grains
265
Fig. 6.39. Law of crack propagation.
4.3. BONDS (BONDING BETWEEN THE LINER AND THE
PROPELLANT)
4.3. 1. Physical and mechanical nature of the
bonds
The bonds represent physically the adhesion occurring during the propel-
lant curing phase, between the propellant and the liner. This adhesion takes
place by the migration through the surface of various products that allow the
creation of physicochemical bonds. A detailed analysis of the material in the
vicinity of the bonds reveals that there is no bondline, geometrically speaking,
but rather a significant gradient of the mechanical properties.
Mechanically, the bonding is represented by a surface separating two
homogeneous materials. Consequently, there is a discontinuity of the stress
tensor and of the strain tensor through the bondline. From a mechanical
point of view there is a continuity of the displacement of all surface points
belonging both to the liner and to the propellant, and of the force applied to
the surface. All other components are discontinuous.
On the bondline, the force per unit surface is the sum of an elongation
component <r N , called normal stress, and a sliding component called shear
stress (Fig. 40).
F = a N • n + xt
266
Bernard Gondouin
F Applied Force at M
relating to bonding plane
Fi et F 2 Applied Forces at M
relating to the plane
normal to the bonding plane
At the point M, there are 2 stress tensors
relating to material (T ) relating to material (5)
On T
1
L^_
T (O,),
T (^1)2
There is continuity of a n and x
Fig. 6.40. Discontinuity in the vicinity of a bondline.
The continuity of the force is expressed by the continuity of the normal stress
and of the shear stress applied to the bondline. These components are
therefore the components that globally characterize the capability of the
bonds.
4.3.2 . Behavior of the bonds
4.3.2. 1. Micromechanical analysis
The micromechanical analysis of the behavior of the material in the plane
area of the bonding is conducted by taking microspecimens on which the
mechanical characteristics under tensile test are determined (Fig. 41). Addi-
tional microhardness tests make it possible to confirm the results obtained on
the small specimens. There is, in some propellant compositions, an increase in
Young’s modulus in the vicinity of the bondline, as well as an increase in
hardness (Figs 42 and 43).
Structural Analysis of Propellant Grains
267
Dimension of the specimens for the micromechanical study
Length * 25 mm Width = 5 mm Thickness = 0,5 mm
Fig. 6.41. Removal of microspecimen in the vicinity of the bondline.
(Tensile rate: 50 mm/min)
0 1 1 1 1 ■*-
50 100 150
Bonding plane Distance to the bonding plane in mm
Fig. 6.42. Evolution of the modulus in the vicinity of the bonding plane.
4.3.2.2. Global analysis
The complex nature of the bonding area having been revealed by the
micromechanical analysis, it is therefore possible to mechanically character-
ize the entire bonding area by assuming that the liner-propellant whole is an
268
Bernard Gondouin
orthotropic material. The symmetry of the superposition of the various
materials reduces to five the number of coefficients that need to be deter-
mined to characterize the behavior (Fig. 44).
4.3.3. Capability of the bonds
The capability of the bonds is obtained by applying increasing load until
failure of the specimen occurs.
4.3.3. 1. Micromechanical analysis
This particular analysis, performed on microspecimens described in Sec-
tion 4.3.2. 1, allows us to discover a variation of the maximum stress at break
and the corresponding strain in the vicinity of the bonding area (Fig. 45).
4. 3. 3. 2. Global analysis
There are two ways of performing the global analysis of the capability:
• by assimilating the bonding area to an orthotropic material;
• by measuring the maximum force applied to the bonding plane.
The first method is simply a prolongation of the method described in Section
4.3. 2.2.
The second method consists of measuring the maximum force applied to
the bonding plane for different application angles. The specimens used are
those described in Fig. 46.
269
Structural Analysis of Propellant Grains
Liner Thermal insulation
I
Fig. 6.44. The bonding area is an orthotropic material.
One can identify, in a plane (a N , r) a curve that limits a high probability
failure area and a low probability failure area (Fig. 47).
The scattering observed in these tests is important.
In most cases the failure in the propellant occurs in the vicinity of the
bonding plane.
The tensile stress specimen used to characterize the bonds (Fig. 46) is not a
monodimensional specimen. The maximum stress obtained at the failure of
the specimen, in the propellant, in the vicinity of the bonding plane, is lower
than the maximum stress obtained on propellant alone from a monodimen-
sional specimen. A tensile test performed on propellant alone with a cubic
specimen used for bonding is sufficient to verify the influence of the geometry
of the specimen.
270
Bernard Gondouin
i i i i
| 5 10 15
| Bonding plane Distance to the bonding plane (mm)
Fig. 6.45. Evolution of and e m in the vicinity of the bonding plane.
4.3.4. Propagation of the debondings; peeling
The characterization of the ability of an initial debonding to propagate is
determined by performing a peeling test. This test is described in Fig. 48. This
test is used to categorize, for various liner-propellant assemblies, the force
necessary for the debonding to propagate itself, for a given loading rate. The
greater the peeling force versus the width of the specimen, the better the
structural integrity of the specimen will be, all other things being equal.
As the debonding propagates itself in the propellant, the results of tearing
in the corresponding propellant can be used to perform a qualitative
correlation.
5. Determination of the Induced Stress-Strain
(Requirement)
5.1. BRIEF BACKGROUND
The determination of the stress existing in a propellant grain subjected to a
mechanical load is vital to assess the safety coefficient of this propellant grain.
271
Structural Analysis of Propellant Grains
Metallic Jaw
Thermal insulation
Liner
Propellant
Metallic Jaw
I
Flanged Cubic Specimen
Tensile load
Device used to determine the failure criterion
Fig. 6.46. Specimens for bonding tests.
This problem has always been, and continues to be, a constant source of
concern. The methods used to resolve it change with the discovery of new
technology.
Until the 1960s experimental methods were widely used. Then, with the
progress made by numerical methods and computers, numerical analysis
became the preferred method. Currently, they are the primary tool, and their
use has modified considerably the steps followed to analyze propellant grains.
Experimental methods did not allow the analysis of geometries that were too
complex. These geometries were the results of the experience — often very
extensive — of the designers, but the optimization from the point of view of
structural integrity was not always possible (because the experimental
methods used were very cumbersome). Computerized methods allow us, on
272
Bernard Gondouin
the contrary, to analyze a great number of geometries and to select the one
geometry that is best suited to solve the problem at hand. The experimental
methods are, nevertheless, still used and developed parallel to the computer-
ized methods to validate experimentally the theoretical analyses.
5.2. THE EXPERIMENTAL METHODS
When a direct measurement of stress/strain in a propellant grain is used, it
usually involves measurements of strains. The analysis of stresses is more
difficult because the gages are for the most part larger and can mechanically
disturb the environment where they are implanted.
The indirect method most widely used to perform indirect measurements is
photoelasticimetry [5]. This allows an experimental determination of the
stress. Some transparent materials have the characteristic of becoming
birefracting when subjected to a stress field. Polyurethane and some of the
epoxy resins have that property. When specimens made of these materials are
subjected to a mechanical loading, interference fringes are revealed when the
specimens are placed between two polarizing and analyzing filters in the path
of a light ray. These fringes are caused by the existence of stresses in the
Structural Analysis of Propellant Grains
273
Sketch of the testing equipment
| Tensile load
sample under study. This method consists of preparing samples made of resin
shaped like the propellant grain or the portion of the propellant grain under
analysis. Reduced scale may possibly be used. A mechanical load is applied to
the sample to obtain stresses identical to those present in the propellant
grain.
The stress state modifies the optical properties of the sample; these
properties are frozen in that particular state by the appropriate thermal cycle.
After this, thin slices are cut — they have kept their birefracting state
corresponding to the mechanical stress field — and analyzed with a two-
dimensional method.
The main difficulties encountered with this method are to obtain the
proper geometry and to apply the stress conditions within realistic boundary
limits. Moreover, the analysis of the stress field is performed in a material that
typically exhibits an incompressible linear elastic behavior.
5.3. NUMERICAL METHODS
The subject discussed in this section has been by itself the object of a
tremendous number of studies for many years. Today, a significant number of
studies continue to be performed. It is therefore not necessary to provide here
a detailed description of numerical methods, since there is a large quantity of
274
Bernard Gondouin
good-quality literature on the subject. Their practical use is discussed in
Chapter 2. Only special aspects of the structural integrity analysis of
propellant grains are listed below.
All mechanical analyses are defined by (Fig. 1):
• a precise description of the geometry to which the mechanical load is
applied;
• the boundary conditions depicting the loading conditions;
• the mechanical behavior law of the materials.
The geometry involved in propellant grain is three-dimensional; the mechan-
ical loads applied are static, dynamic, and with or without thermal effects,
and the behavior laws are non-linear viscoelastic.
Dealing with the mechanical analysis involves resolving the conservation
equations (of the mass, the energy, and the volume for an incompressible
material) and the equilibrium equations of the forces and the vectorial
moments, taking into account the boundary conditions applied. All of these
equations are expressed, in the end, in differential equations for the displace-
ments. The numerical method used is the finite element method. Without
going into great details about this method, the subject of an abundant
specialized literature ([6] and [7] among many others), the principle may be
succinctly described as follows:
The geometry is decomposed into a finite number of small areas (called
finite elements) where the function to be determined (the displacement field)
is expressed by a function of the coordinates of the points of the areas. This
function is usually a polynomial of the first or second degree.
When dealing with propellant grains there is the additional problem of
incompressibility. Let us consider the formulation expressed by equations (4)
Wu = 2 Ge' (j
\ 5 =3 Ke
The volume conservation equation (incompressibility assumption) in the
case of infinitesimal deformations is expressed by e = 0.
Consequently, the mechanical problem is solvable only to determine the
deviatoric tensor, the average stress is indeterminate. There have been a
number of methods proposed to determine the average stress. Some iterative
methods do not give satisfaction in all cases studied. There is, however, one
method particularly well suited for structural analysis of propellant grains.
This was developed by Herrmann [20] and consists of assuming the average
stress d to be an unknown in the problem. There are therefore two types of
unknown to determine: displacement unknowns and average stress d un-
knowns.
With the finite element method, the structural analysis is generally
performed with linear behaviors of the propellant. The methods that include
nonlinear behaviors take an inordinate amount of time for the calculations.
In Section 2, however, the description of the mechanical loads imposed on
Structural Analysis of Propellant Grains
275
propellant grains shows that, in the worst conditions (temperature changes
and pressurization at firing) and because the propellant is an incompressible
material, the strain field in the propellant depends little on the mechanical
behavior law. Consequently, the analysis can be performed in the following
manner (Fig. 49):
1. calculations are done using the linear and incompressible behavior law to
determine the strain field;
2. at the point where the elongation is the greatest, the stress tensor is
recalculated, using a behavior law that is more representative for the
propellant.
Nowadays, the finite-element computer programs that allow a correct
handling of the problems of propellant linear behavior are the programs that
have the following characteristics:
• programs dealing with the propellant incompressibility with the Herr-
mann method;
• types of solid elements:
— in two-dimensional, elements with eight nodes with the Herrmann
formula;
— in three-dimensional, elements with 20 nodes with Herrmann for-
mula;
— skin elements to determine stress tensor at free surface.
Fig. 6.49. Calculation of the induced load for a non-linear viscoelastic behavior.
276
Bernard Gondouin
The quality of a computer program depends on the structural analysis itself,
but also, and most particularly, on the quality of the tools used to prepare
and analyze the calculations. These tools are called pre- and post-processors.
There is no particular interest in describing these tools here, except for saying
that they are extremely useful. They have a great value for a rapid implemen-
tation and rational utilization of computer programs for mechanical analysis.
The level of professionalism of the designers is often dependent on the quality
of these tools.
Figures 50 to 54 provide a summary of the possibilities offered by these
analysis methods, without which today’s advanced mechanical analysis could
not be done.
5.4. SIMPLIFIED ANALYTICAL METHODS
For preliminary design analysis, analytical methods are useful when the
geometry of the propellant grains can be likened to a specific one-dimen-
sional geometry: the infinite-length hollow cylinder.
The stress/strain and displacements are expressed in a cylindrical coordin-
ates reference system (r, 0, z). The mechanical state of a cylinder under a
specific mechanical load is described by 15 quantities.
Fig. 6.50. Determination of the induced load. Three-dimensional mesh I.
Fig. 6.52. Iso-stresses I. (On skin elements.)
278
Bernard Gondouin
Fig. 6.53. Iso-stresses II. (On a section plane.)
Fig. 6.54. Iso-stresses III.
• six stress components: a rr , a ee , a zz , a r6 , a rz , a 6z
• six strain components: e rr , e e(h e zz , e r0 , e rz , e 0z
• three displacement components: w r , w z
In an infinite-length cylinder, the displacement at each point is expressed by
only one component w r ; it is a plane strain assumption:
u e = o, u z = o and u r = u r (r )
d u r u r
=> e z = o, e r = — e e = -
dr r
and for axisymmetric boundary conditions:
£ r0 = E 0z ~ £ rz = ®
= O
Structural Analysis of Propellant Grains 279
When the material is assumed to be incompressible, Hooke’s thermoelastic
law is written as:
+ ^aAT (26)
+ l«AT
2
where:
E = Young’s modulus;
a = linear thermal expansion coefficient of the material;
AT =T - T 0 ;
T = temperature at which the stress occurs;
T 0 = equilibrium temperature (at which stress is zero).
The equation of equilibrium is written:
£ rr — ( G rr G dd)
& ee = ( a ee ~ °rr )
dOff
dr
(27)
and the strain-displacement relation
dzee
(28)
From eqns (26), (27) and (28), we can write:
3 00 ~ °rr )
4 E
dr
+ ( G 00 ~
g(l/£) 3
dr 2 E
']
3 „ da AT
+ -£ — = » (2S)
For a hollow circular cylinder with
a: inside radius
b : outside radius
the general solution is written:
f r 2 E C r 2 E C r l
^rrOO = 5 - F(r)dr + F(a) r dr + Ci -
J a J a J a ^
IE C'
°ee(r) = ~ ~j \
’ J a
E J ,
3 dr +
docAT
dr + Ci -2 + <r r r(r)
(30)
(31)
Ci and C 2 are integration constants determined by the boundary conditions.
F(r) is the primitive of r 2 (da A T/dr).
280
Bernard Gondouin
When the temperature is uniform and the modulus constant in the entire
geometry, the general solution will be:
tfrrO) = C l~^J ( 32 >
<j ee (r) = c ! + ^ (33)
C { and C 2 are determined by the boundary conditions.
5.4.1. Uniform thermal shrinkage in a case-
bonded cylinder
When the propellant is bonded to an non-deformable, rigid motor case,
with a very small linear thermal expansion coefficient when compared to that
of the propellant, the boundary conditions will be expressed by:
o rr (a) = o, because the inside surface of the cylinder is a free surface;
u r (b) = o, e e6 (b) = o, because there is no displacement of the propellant
points bonded to the case.
Consequently:
(T » = E h ~2 ^
b 2 ( a 2 \
G gg (r) = E~i 1 + jj) (34)
£f>f>(r)= ~^ aAT (~2~ ^
• The circumferential strain e dd is maximum in the central port at r = a.
£««(«)= ~\ aAT (~2~ 1
• The normal stress o rr is maximum at the propellant/case bonding at
r = b.
(b 2
o rr (b)= —EocAtI^z “ 1
With this type of geometry and a mechanical load corresponding to a
uniform thermal shrinkage, strains are independent of the propellant Young’s
modulus and stresses are directly proportional to that modulus. Stress at the
free surface and at the bonding, in addition, is dependent on b 2 /a 2 . The
Structural Analysis of Propellant Grains 281
volumetric loading fraction expressed by the ratio b 2 /a 2 , will have an
important effect on the stress.
Propellant grains have a finite length. There are corrective factors [27]
allowing the determination of the stress tensor in a finite-length circular
cylinder. These factors are given in diagrams (Parr diagrams).
All stresses/strains for this type of mechanical load are proportional to the
aA T product. That is why a, the linear thermal expansion coefficient of the
propellant, must be well determined.
5.4.2 . Internal pressure p on a case-bonded
cylinder
When the motor case in which the propellant grain is located is a thin one,
the boundary conditions are written as:
aAT = o
tfrrfa) = ~P
e ee (b) = —ka rr (b)
where k is the flexibility coefficient of the case
(1-v,
£ c *
v c = Poisson’s ratio of the motor case;
E c = Young’s modulus of the motor case;
h = thickness of the motor case.
For a motor case showing little deformation (k is very small), simplifica-
tions allow us to obtain:
£ee(r) = -e„ r (r) = kp~^
tfrrM = \ k P E (^2 -JS -\~P ( 35 )
, v 2, Jb 2 b 2 \
°ee(r) = ^ k P E [~ 2 + ^ J ~ P
As with the thermal load, strains are independent of the propellant Young’s
modulus, and stresses are proportional to that modulus. The loading ratio,
when it grows, increases the level of the stresses in the propellant. Finally, the
induced stress/strain depends greatly on the flexibility coefficient of the motor
case. The smaller the flexibility coefficient, and consequently the higher the
Young’s modulus of the motor case, the lower the induced stress/strain will
be.
282
Bernard Gondouin
5.5. COMMENTS ON THE NECESSITY OF INCOMPRESSIBLE
ANALYSES
The mechanical analysis of incompressible materials involves a discontin-
uity which is expressed with a special formula. A material is considered
incompressible when it sustains a deformation while maintaining its constant
volume under the effect of applied mechanical load. Based on this definition,
the particularity of the incompressibility characteristic does not seem evident.
But a deformation under constant volume implies that the material has been
provided with a shape that allows such a deformation. The amount of free
surface has a determining impact on the rigidity of the object. For example: a
viscous liquid has no rigidity; a flexible polyethylene bottle has a low rigidity
when it is empty. When that same bottle is completely filled with viscous
liquid, the combination exhibits a rigidity under pressure that allows an
integral transmission of loads. This is the basic principle which allows
hydraulic systems to transmit significant energy quantities.
Incompressible materials are, therefore, sensitive to confinement, which
can be defined by the ratio of the volume of the object versus the surfaces free
to sustain deformation. An infinite confinement corresponds to an infinite
rigidity of the object. This is the meaning of the discontinuity mentioned at
the beginning of this section.
• What is the effect of incompressible behavior on the equations?
Based on eqns (1) and (4), assuming infinitesimal deformations, constant
volume deformations imply the following relation:
AV *
TT-I% = 0
y 0 i = 1
which, in terms of the behavior parameters, is expressed by:
G
v = 0.5 or K -* oo as — — ► 0
therefore the stress deviator is determined directly by the existing strain field,
but the average stress is mathematically undeterminate.
(f = Ke with K — ► oo
e = 0
This average stress is determined physically by the geometry and the
confinement.
• In fact, the measurement of the bulk modulus of a propellant gives a finite
value; this value is very high in comparison with the value of the shear
modulus. It is that significant difference between the compressibility
modulus and the shear modulus that confers the incompressible property
to propellants.
• What is the behavior of a propellant in the shape of a grain?
Structural Analysis of Propellant Grains
283
Consideration of the incompressibility is of concern only with case-bonded
propellant grains. Typically, this type of propellant grain has a higher
volumetric loading fraction. All of the propellant surfaces are bonded to the
motor case; the only free surfaces are those in the combustion chamber. The
higher the volumetric loading fraction, the greater the confinement of the
propellant will be.
In general, stresses induced by thermal shrinkage and by pressure rise at
the beginning of firing are the most severe.
The average level of strain is often lower than the strain at which vacuum
holes occur (i.e. at which the propellant becomes compressible).
Only a small volume of the propellant has a significant strain level, making
it compressible. This low volume of compressible propellant (with vacuum
holes) does not modify the incompressible behavior of the major portion of
the propellant. Simple calculations (Fig. 55) show that because the volume of
propellant with vacuum holes is low, the maximum induced stress/strain can
be determined by assuming that the entire propellant is incompressible. This
is particularly applicable to the stress/strain induced by thermal shrinkage; at
the time of firing, the behavior of propellant under pressure likens it to an
incompressible material, whatever the level of applied load.
It is therefore necessary to take into account the incompressible nature of
the propellant to evaluate induced stress/strain in case-bonded grains, and it
is the determination of average stress at each point which allows an accurate
mechanical analysis. The average stress is not dependent on the propellant
behavior, and a mechanical analysis taking into consideration the incompres-
sible elastic linear behavior of the propellant is sufficient. The viscoelastic
properties may be introduced to calculate the stress deviators.
Some calculations based on a simple geometry allow us to summarize the
importance of incompressibility.
The geometry used is an infinite length cylinder with an inner diameter of
100 mm and an outer diameter of 400 mm. A temperature change of — 100°C
is induced. The external surface of the cylinder is bonded to a rigid, non-
deformable case. The calculations are done with a finite element program
including Herrmann’s formulation to treat incompressible behavior. This
program also includes classic elements, allowing it to process compressible
materials. In addition, the elements with the Herrmann formula allow the
processing of materials with any Poisson’s ratio, including v = 0.5.
First analysis. The impact of Poisson’s ratio on the infinite-length cylinder
is indicated in Fig. 56.
The induced stress is represented by an equivalent stress (Stassi stress),
which takes the average stress into account; it is at a maximum on the free
surface and is heavily dependent on the value of Poisson’s ratio (Fig. 57).
Second analysis. The propellant is considered to be very compressible
(Poisson’s ratio equal to 0.33), and the analysis is done with two types of
element: the classic element and the Herrmann formula element. The results,
284
Bernard Gondouin
Curvilinear abscissa
Curvilinear abscissa
Fig. 6.55. Calculation without and with compressible volume. (Plane strain assump-
tion.)
when compared to the analytical solution, reveal a high level of correspon-
dence between the numerical analysis and the analytical solution (Fig. 58).
Third analysis. Finally, a third analysis is performed, for propellants
exhibiting a low compressibility (v = 0.495).
A low-compressibility element can be analyzed with a classic element. The
results listed in Fig. 59 show good agreement between the analytical solution
Structural Analysis of Propellant Grains
285
Radius (m)
Fig. 6.56. Influence of Poisson’s ratio on the equivalent stress.
Fig. 6.57. Influence of Poisson’s ratio on the equivalent stress on the free surface.
and the analysis done with the Herrmann’s formulation. Results obtained
with the classic elements are completely erroneous.
The Von-Mises stress, which depends solely on the stress deviators and not
at all on the average stress, is analyzed with two types of elements:
• the classical element formulated in displacement;
• the Herrmann formula element.
Equivalent stress (10 5 Pa)
286
Bernard Gondouin
Infinite Length Cylinder DT = -100
Compressible NU = 0.33
2nd degree displacement + Herrmann's Formulation
^ a o »
a- 45 .. 9 a 1st
o \ — Analytical solution
0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Radius (m)
Fig. 6.58. Comparison of Herrmann’s formulation and classical formulation
applied to a compressible material.
45 ^ o 0
Infinite Length Cylinder DT = -100
Compressible NU = 0.495
2nd degree displacement + Herrmann’s Formulation
— Analytical Solution
0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.2
Radius (m)
Fig. 6.59. Comparison between Hermann’s formulation and classical formulation
applied to a quasi incompressible material.
Structural Analysis of Propellant Grains
287
The good agreement between both numerical analysis and analytical solution
(Fig. 60) demonstrates that correctly solving an incompressible problem
consists in determining the average stress at each point.
6. Determination of the Factor of Safety
Following the description in the preceding sections of the methods used to
determine the capability and the induced stress/strain, the next logical step is
the determination of the structural factor of safety:
In fact, the problem is really complex, because a propellant grain is
subjected to very varied mechanical loads, and the cumulation of the
corresponding induced stress/strain complicates the determination of a factor
of safety. The capability of the propellant of a case-bonded grain which
experiences temperature changes from 50°C to 20°C in a few days, which is
then subjected to the force of gravity over a period of several months, and
which finally is subjected at the time of firing to a pressure rise in a few
milliseconds, is difficult to determine.
With a cumulation of mechanical stresses, the difficulty resides in the
definition of the capability that should be taken into consideration. The
20
18
16
14
12
a io
8
6
4
2
VON-MISES Stress
Nu - .499
+ Displacement
o Herrmann
— Analytical
0i i i * i 1 i i i i 1
0 0.02 0.06 0.10 0.14 0.18
Radius(m)
Fig. 6.60. Comparison of the deviatoric stresses obtained by the Herrmann’s formu-
lation and the classical formulation in a quasi incompressible material.
288
Bernard Gondouin
induced stresses/strains can be combined using the classic additivity laws
(making sure that the components of the stress and strain tensors are added
only when they are expressed in the same coordinates system).
One method used to assess the capability resulting from the cumulation of
mechanical loads consists in submitting a propellant specimen to a succes-
sion of mechanical loads experienced by the propellant, under identical
temperature, pressure, and loading rates. This highly experimental method
does not always permit the determination of real operation conditions of a
propellant, because it would require the use of very heavy and costly test
facilities. A low-speed tensile stress, for example, applied while simultan-
eously varying the temperature, and followed by a rapid and progressive
increase of pressure from 1 to 10 MPa, is not a simple operation to carry out!
Another method consists of defining the factor of safety of each of the basic
mechanical loads, such as temperature changes, the force of gravity, the
pressure rise at firing, and others, after which the resulting factor of safety will
be a function of each basic factor of safety. Nevertheless, whatever the method
used, the factor of safety calculated from stresses or strains must be equal to 1
at grain rupture and, similarly, the reliability calculated using each of the
methods must be identical. It is therefore of prime importance to verify each
of the methods on reduced-size objects subjected to various mechanical loads
leading to failure.
The methods used to calculate the factors of safety are described below.
Tests are performed on simple geometries to compare these methods, and
eventually improve them. They are described at the end of this section.
6.1. FACTOR OF SAFETY OF PROPELLANT GRAINS
6.1.1. Factor of safety in cumulative damage
theory
Damage, described in Section 4.2.7, characterizes the damage done to
propellant during its useful life. By definition, it varies over time from 0 to 1 :
@(o) = o Corresponds to sound propellant grain after its manufacture;
@(t R ) - 1 Corresponds to the failure of the propellant (failure time t R ).
The factor of safety is simply deduced from damage 3){t) using the relation
K®(t) =
1
W)
(36)
Defined in that manner, the factor of safety varies over time from infinity to 1.
Fundamental studies on propellants combustion requires
sophisticated hardware because of the very extreme conditions of
temperature, pressure, gas velocities existing in the combustion
chambers of solid rocket motors. The photograph shows the
observation of tangential acoustic instabilities - mode 3 - in the
section of a star-shaped grain.
Robot for filling a motor case with
casting powder for CDB propellant
(SNPE - Angouleme plant).
!?!■' . ” • ij
PRODUCTION TECHNOLOGIES The industrial equipments
used in the solid propellants industry are characterized by the great
number of various technologies used and the high investment costs,
because of the necessity to have, for safety reasons, a lot of remote
controlled operations and important protections. The left page
Twin screw continuous extrusion of
double base propellants (SNPE -
Saint-Medard-en-Jalles plant).
\ r m— ■
-+ lltmHMr' Li
Machining of a big propellant grain
(SNPE - Saint-Medard-en-Jalles
plant).
■■■■■■■
jj Nitric esters production plant (SNPE -
f Angouleme).
UDMH (unsymmetncal dimethyl
hydrazine) production plant for Ariane
Viking motors (SNPE - Toulouse plant).
illustrates the batch mixing of a solid propellant. The mixer’s bowl
is lowered and the blades are visible. The right page shows a typical
radiographic facility for inspection of big propellant grains (SNPE —
Saint-Medard-en-Jalles plant).
Composite propellant case-bonded
motor for an air to ground rocket.
.
INNOVATION Constant requirements for the improvement of
missiles and space boosters performances lead to the necessity of
progress on every subsystem, and specifically on propulsion
systems. While the very successful EXOCET antiship missile
■■■■■■■Mi
SNPE Production
INDUSTRIALIZATION Solid propellant grains are designed
according to requirements for various different missions. These
designs use a great variety of shapes,, masses, dimensions and
propellant formulations. This page illustrates the main propellant
anti-tank
missiles
f
anti- runway
rockets
9UMACCPACU> SS11 HOT MILAN
SEP TK BRANDT
duction
ler licence
strategic
ballistic
missiles
■ SD
■ EPICItTE
□ COMPOSITE
□ NITRAMITE
space launchers
HAWS MLRS
S3 M4
NATO MAWS EPG
in
DEFENSE ESPACE
Air to air missile motor.
CWR
Motor j fupttttl Soldo P
Internal view of a segmented space
launcher booster.
grains under development and production at SNPE in 1988. The
scale of propellant masses involved goes from a few grams
(thrusters) to a few hundred tons (ARIANE 5 solid boosters).
SOPHISTICATION The methodologies, equipment, R and D
work used in the solid propulsion industry have always used the
higher performing technologies of the time... The importance and
of its applications, the constant - requirement for improved
KBs*-'
mm
Graphic display of the structural
' analysis of a case-bonded propellant
grain.
Physico chemical analysis of solid 1
propellants.
performances, justify the use of the most sophisticated equipments,
This is particularly illustrated by the Submarine Launched Ballistic
Missiles.
■I
‘
\ -
Mandrels of different shapes for
molding the bore of solid propellant
grains.
Casting pits for composite propellant
for big motors (SNPE - Saint-
M6dard-en-Jalles).
Modem production plants for solid propellants are more and more
specialized, integrated and automatized, at least when the quantities
to be produced justify the investment. The right page shows the
integrated facility used for the production of MLRS motors (SNPE
- Saint-Medard-en-Jalles).
Structural Analysis of Propellant Grains
289
In Section 4.2.7 an expression was suggested for the damage from
experimental results obtained from creeping tests (eqn 24):
m
\ l/m
[(7 0 (T)] m dT )
)
This equation calls for several remarks:
Remark 1. The factor of safety defined from eqn (24) is written:
**(0 = W *
( % t \ 1 fm
[0- o (T)]"dTj
(37)
In this relation: \/@> Q represents the capability of the propellant; it is an
experimental datum.
(jW:n-d<r
stands for the induced stress in the propellant grain; it is a value obtained by
calculations.
K 3 is, in fact, the ratio of a capability to an induced stress.
Remark 2. Equation (24), providing a damage type, can also be written in
the following manner:
imr = m = &* f c^rdt (38)
Jo
D{t) varies from 0 to 1, and therefore corresponds to another expression of
the damage that has the same definition.
In fact, eqn (38) is the equation that corresponds to the initial definition of
the damage, and best expresses the physical phenomenon. For example, in a
tensile test during which the stress varies in a linear fashion over time, the two
types of damage are written:
/ l \l/m
m =
i
m + 1
t"
i
The plotting of these two forms of expression is given in Fig. 61 for a
realistic value of parameter m(m = 10)D(f), representing a linear cumulation
of the damage, and demonstrates the fact that the damage sustained by the
propellant is very low up to a fairly high value of the stress, relative to the
maximum stress a m .
290
Bernard Gondouin
£>(')
D(.)
Fig. 6.61. Damage for a linear evolution of the stress.
For example, if the propellant is to be subjected to stress cycles, illustrated
in Fig. 62, during which the stress varies between 0 and a m , where cr m is the
maximum stress for the tensile test at the same stress rate, and a the
coefficient ranges from 0 to 1, the number of cycles N it can withstand is
dependent on the value of the coefficient a and is given, based on eqns (24) or
(38), by:
N =
With a realistic value for m(m = 10), the values obtained are indicated in
Table 2.
Fig. 6.62. Stress cycles imposed on a specimen.
Table 2
a
Number of cyles
0.5
2048
0.8
-11
0.9
-3
Structural Analysis of Propellant Grains
291
Under these conditions the damage sustained by the propellant for a 0.5 o m
cycle is negligible in comparison with the damage sustained at a 0.9 o m cycle.
Remark 3. Strain damage can be defined based on experimental results
obtained from relaxation tests, for various strains, up to failure. Typically, the
formula is very close to that given by eqn (24) but the value of exponent m is
greater (m > 30).
Similarly, the factor of safety is given by the inverse of the damage.
Remark 4. The cumulation of induced stresses/strains presents no problem
when the factor of safety is calculated in terms of damage, because the
induced stress/strain is integrated over time, and the capability, represented
by 1/0 O , is representative of multiple tests performed under very varied
conditions. The use of the factor of safety in terms of damage seems, therefore,
to resolve all cumulation problems. Although it is certainly the factor that
deals best with the problem, it should not be forgotten that eqn (24) is a
simple equation applied only when the creep failure curve is a straight line
(log a F = A log t K 4- B). In propellants, the equations expressing the damage
are usually more complex (eqn 25) and, in any case, they must be experimen-
tally determined and verified for each propellant.
6. 1.2 . Factor of safety defined with strains
For an elementary mechanical load, this is defined by:
K. = - (39)
£ 0
where:
e m = strain under tensile stress relative to the maximum stress, for the
parameters of loading rate and temperature corresponding to the
applied mechanical load;
e 0 = strain corresponding to the point where the induced strain is maxi-
mum; it is determined from the equivalent stress, assessed with the
failure criterion, for a Young’s modulus E that corresponds to
parameters of loading rate and temperature of the mechanical load:
This definition of equivalent strain implies that the multidimensional
effects are the same for stresses as for strains. In particular, the effect of
pressure must be identical for the stress capability as for the strain capability
(see Section 4.2.4.).
One method for the cumulation of basic factors of safety determined for
strain is obtained from remarks 2 and 3 of the preceding section. When m is
292
Bernard Gondouin
very large (1/m close to 0), the initial definition of damage can no longer be
used because, during a relaxation test, the failure time tends to be infinite.
Damage, in this situation, is written in other forms, including:
where:
Of = max
(40)
e OI = equivalent strain sustained by the propellant grain for an elementary
mechanical load i ;
e m i = strain at failure of the propellant grain for the elementary mechanical
load.
K =
(41)
This relation is correct in the case where, after each basic load, the induced
strain returns to a zero value (Fig. 63).
But in the case of mechanical load increments (Fig. 64) this relation is not
applicable. In this case, the damage could be expressed by:
N Ae -
X —
i = 1 ‘'mi
(42)
Ae oi = Equivalent strain increment resulting from mechanical load i;
e mi = strain capability at mechanical load i .
Therefore, the factor of safety is written as:
K =
1
N Ae ■
y “~“oi
Fig. 6.63. Cumulation of mechanical loading.
293
Structural Analysis of Propellant Grains
Fig. 6.64. Loading increments.
The calculation of the factor of safety based on the strains presents a very
distinct advantage for case-bonded grains. In these grains the two important
mechanical loads are due to temperature changes and pressure rise at firing.
For these mechanical loads the strains are not dependent on the behavior of
the propellant when it is used in its incompressible portion.
That is why research continues, so that a relation can be determined which
takes the cumulation of strains into consideration, specifically in the case of
tensile stress with simultaneous temperature changes [34].
6. 1.3 . Factor of safety defined with stresses
For an elementary mechanical load, this is defined by:
= ~
<*0
where:
<r m = maximum stress for the loading rate and temperature parameters
corresponding to the applied mechanical load;
cr 0 = equivalent stress at the most stressed point, assessed through calcula-
tions using the failure criterion.
The cumulation of induced stresses presents the same problem, whether the
basic factors of safety were determined from the stresses or the strains.
It is possible, however, to establish empirical rules based on observations
made in the course of simple tests, provided that these rules constantly
remain subject to revision.
The following rule can be proposed
g o (0
K,
294
Bernard Gondouin
where:
cr o (0 = stress cumulation existing in the propellant grain at time t ;
a m (t) = stress capability of the propellant under the total load conditions
at time t.
Unfortunately, with a case-bonded grain, the induced stresses are often
dependent on the behavior of the propellant; consequently, to obtain a
reliable factor of safety, it is important to know that behavior.
6.2. BONDING FACTOR OF SAFETY
The assessment of the safety factor of the bonding is always done using
stress. Several failure criteria can be used for bondings:
• normal stress criterion;
• shear stress;
• surfacic force applied at the bondline (<r N , t).
In every case the factor of safety is defined by the ratio between the capability
(obtained experimentally as described in Section 4.3.3) and the induced stress
using one or the other failure criteria.
The failure criterion expressed in force seems to be best suited.
In every case the factor of safety in relation to the propellant is calculated
at the critical point of the bonding. When it is found to be smaller than one of
the factors of safety obtained from the bonding failure criteria, it is used to
characterize the bonding.
In the case of the induced stress resulting from firing, the importance of the
effect of the pressure varies, based on whether the grain has been stress-
relieved (prepared debonding), or completely bonded. For a stress-relieved
grain the most stressed point of the bonding is located fairly far from the
burning surface. Should debonding occur during pressure rise, the propellant
is pressed again against the liner and the risk of propagation is rather low. In
addition, since the flame reaches the debonding at the end of the firing, the
operation of the motor is not affected.
But in the case of an entirely bound grain, the critical point is located very
close to the free surface, i.e. the combustion chamber. A debonding in that
area has a high level of probability of opening into the combustion chamber
creating at the time of firing an additional burning surface, and therefore a
faulty operation of the motor (Fig. 65). In this case the effect of the pressure
on the normal stress must be taken into account.
Comment. As with propellant (Section 6.1.1.) there is the problem of
damage cumulation for the propellant-liner bonds. Research is being done in
that area [28]. The cumulative damage laws described in Section 6.1.1 can,
however, be used for the propellant-liner bonds, even though the bond
failures always occur in the propellant.
Structural Analysis of Propellant Grains
295
Defect that
does not open
to the surface
Defect opening
to the surface
Evolution of the flame front
Fig. 6.65.
6.3. VERIFICATION AND ADJUSTMENT OF VARIOUS
METHODS OF ANALYSIS OF FACTORS OF SAFETY
Verification of the methods cannot be done on a large number of
propellant grains when these are either expensive or of large size.
It is therefore desirable to design objects that are small in size, inexpensive,
simple to use, and allow the creation in the propellant of induced stresses/
strains identical to those occurring in propellant grains. Several objects, of
varying geometry, have been proposed, including the SEC model developed
in the United States [29], and the PHI model from France [30] (Figs 66 and
67).
These objects are subjected to various thermal cycles or to pressurizations
until the propellant fails. These are used to evaluate the various methods used
to calculate the factor of safety in the case of cumulative mechanical stresses.
Case
Propellant
Fig. 6.66. S.E.C. model.
296
Bernard Gondouin
The PHI model offers the distinct advantage of very different induced load
levels simply by modifying several geometrical parameters (Fig. 68):
• inside diameter;
• diameter of the hole in the membrane;
• thickness of the membrane;
• length of the model.
In addition, as it is the case for many propellant grains, the location of the
most stressed point in the PHI model is clearly known, and the volume of
propellant heavily stressed around that point is small in comparison with the
total volume of the propellant. On the other hand, in the SEC model, the
volume of propellant heavily stressed is much larger.
L = 1000 mm
L = 600 mm
Fig. 6.68. Maximum strain as a function of the geometry of the PHI model.
Structural Analysis of Propellant Grains
297
6.4. SEMI-EXPERIMENTAL DETERMINATION OF THE FACTOR
OF SAFETY
When dealing with propellant grains with a complex geometry, subjected
to induced stresses/strains for which it is difficult to develop models (thermal
cycles, for example), semi-experimental methods can be used to calculate the
factor of safety.
Phase 1. A finite element analysis is done on the three-dimensional geo-
metry with an incompressible linear elastic behavior, for a simple mechanical
load (uniform temperature change, for example), and the strain field is
determined.
Phase 2. A PHI model is selected (Fig. 67). Its geometrical dimensions are
such that they allow the same strain level under the same analysis conditions:
same behavior law, same boundary conditions.
Phase 3. The PHI model is made with the propellant that needs to be tested.
It is subjected to the same cycles as the propellant grains being analyzed.
If the specimen breaks during the cycling, the factor of safety propellant
grain is lower than 1. It will therefore be necessary to modify either the
propellant or the geometry of the grain.
If the specimen does not fail, it is subjected to a N number of cycles,
identical to the preceding one, until failure occurs.
If the propellant obeys a damage law of the form (24), one can write, for a
cycle:
and
K = N 1/m
This allows us to determine the order of magnitude of the factor of safety.
The steps involved in this method are shown in Fig. 69.
7. Propellant Behavior Under Dynamic Loads
7.1. LOW AMPLITUDES
Propellant grains are subjected to this type of load during transport or
during a defective operation of the rocket motor (combustion instabilities, for
example). The loads, in these conditions, can be written in terms of Fourier
298
Bernard Gondouin
Fig, 6.69. Semi-experimental determination of the factor of safety.
series, and the propellant behavior is determined as a function of the
frequency. Two methods are used:
• viscoanalyzer (1-1,000 Hz);
• ultrasounds (0.5-2.5 MHz).
The expression of the modulus of a propellant under harmonic stress
loading takes the form of a complex number.
£* = E + iE"
E”
tgd = — expresses the damping of the material.
E
Figures 70.1 and 70.2 illustrate the aspect of the master curve of the
dynamic modulus with which the time-temperature equivalence principle
can be applied.
Structural Analysis of Propellant Grains
299
Specimen:
Shape: Cylindrical
Height: 20 mm
Section: 78.23 mm 2
Stimuli:
Tensile-compression
FREQUENCES
+ 7.8 H z
*<125.H Z
o15.6 H z
° 250. H z
<31.2 H z
■ 500. H z
x 62.5 H J
□1 000. H z
Fig. 6.70(1). Dynamic tests. Viscoelasticimeter.
7.2. HIGH AMPLITUDES
The propellant grains may be subjected to rapidly varying loads, usually
considered as shocks. These are loads that could have a dynamic impact, very
high amplitudes, rendering Fourier series analyses useless because behavior
non-linearity occurs. These loads may cause a fragmentation of the propel-
lant. When these fragments are smaller than a critical size, a transition phase
may occur in the combustion regime for some propellants, leading to a mass
detonation of the rocket motor.
These studies are all concerned with the safety of the motors; they are
discussed in Chapter 7. The experimental methods that help characterize the
propellant behavior are as follows:
• rapid tensile loading machine with a displacement rate of 20 m/s;
• Hopkinson bars;
• impact against flat wall;
• shock Hugoniot measurements with a light gas gun.
The study of the impact behavior on a propellant is discussed in many
research papers ([31-33], among many others), and could fill an entire
300
Bernard Gondouin
chapter. A detailed description of the result of these studies cannot be given
here. It is important, however, to indicate that in the case of composite
propellants, the behavior of the crystalline oxidizers has a major effect on the
behavior of the propellant, while in the case of static loads, whose rates are
much lower, the propellant behavior is mostly dependent on the bonding
between the binder and the crystalline oxidizer.
8. Conclusions and Future Prospects
With a method which would allow a precise determination of the factor of
safety of a propellant grain it would be possible to optimize the performance
of rocket motors through a potential increase in the volumetric loading
fraction of the grain.
Structural Analysis of Propellant Grains
301
The methods used nowadays are still somewhat imprecise in some cases,
and need to be improved. They have, however, made it possible to improve
propellant grain designs. Even though there is no perfect model of the
propellant behavior, the research work has helped us obtain a better
understanding of the phenomena and, indirectly, assisted in the formulation
of new compositions.
A high level of activity must be continued in this area to model the
behavior of propellants and their fracture mechanisms. At the same time,
numerical analysis techniques must evolve further to take the actual propel-
lant behavior into account, at the lowest possible cost.
Finally, all of the research must be based on many experimental results
obtained from tests performed on propellant grains or models.
Bibliography
1. Persoz, B., Introduction a f etude de la rheologie . Dunod.
2. Christensen, R. M., Theory of Viscoelasticity: An Introduction. Academic Press.
3. Ferry, J. D., Viscoelastic Properties of Polymers. Ed. J. Villey, 1970.
4. Farris, R. J., Development of Solid Rocket Propellant Non-Linear Viscoelastic Constitutive
Theory. AFRPL-Tr-75-20, May 1975.
5. Paraskevas, Etude theorique et experimentale de la photoelasticimetrie tridimension nelle.
Rapport CETIM No. 15 G 151.
6. Zienkiewicz, O. C., La methode des elements finis (traduit de la 3eme edition anglaise).
McGraw-Hill.
7. Touzot, G., Une presentation de la methode des elements finis. Presse de FUniversite Laval
(Quebec).
8. Martin, Ch., Racimor, P., Le Roy, M. and Quidot, M., Representation par des lois de
Farris du comportement viscoelastique non lineaire d’un materiau charge. Groupe Frangais
de Rheologie. December 1980.
9. Meli, G., Thepenier, J., Pasquier, M. and Dubroca, G., Mechanical design of case bonded
CMDB grains by a non linear viscoelastic method. AIAA, SAE, and ASME Joint Propulsion
Conference, Vol. 16, No. 80-1177, 1980.
10. Williams, M. L., Landel, R. F. and Ferry, J. D., The temperature dependence of relaxation
mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc .,
77(3), 701, 1955.
11. Boley, B. A. and Weiner, J. H., Theory of Thermal Stresses. 1st edition. John Wiley, New
York. 1960.
12. Reismann, H. and Pawlik, P. S., Elasticity Theory and Applications. John Wiley and Sons.
13. Francis, E. C. et al . , Propellant Non-Linear Constitutive Theory Extension: Preliminary
Results. UTC/CSD-2742-AFRPL-TR-83-034, August 1983.
14. Tschoegl, N. W., Failure Surfaces in Principal Stress Space. Polymer Science Symposium
No. 32, 239-267. John Wiley and Sons. 1971.
15. Langlois, G. and Gonard, R., New law for crack propagation in solid propellant material.
J. Spacecraft Rockets, 16 , 357, 1979.
16. Nottin, J. P,, Gondouin, B. and Lucas, M., Experimental investigation of cracks growth in
composite propellants. AIAA 85-1437. AIAA/SAE/ASME/ASEE 21st Joint Propulsion
Conference. Monterey, California, 1985.
17. Schapery, R. A. Int. J. Fracture, 11 , 141, 1975; International Journal of Fracture, 11 , 369,
1975; Int. J. Fracture, 11 , 549, 1975.
18. Knaus, W. G., On steady propagation of a crack in a viscoelastic sheet: experiments and
analysis. Deformation and Fracture of High Polymers, edited by J. Henning Kausch, Hohn A.
Hassel and Robert K. Jaffee. Plenum Press, 1974.
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19. Beckwith, S. W. and Wang, D. T., Crack Propagation in Double-Base Propellants. Hercules
Incorporated Bacchus Works, Magna, Utah.
20. Herrmann, L. R., Elasticity equations for incompressible and nearly incompressible
materials by a variational theorem. AIAA Journal , 3, 1886-1900, 1965.
21. Shaper Y, R. A., A Micromechanics Model for Non-Linear Viscoelastic Behavior of Particle-
Reinforced Rubber with Distributed Damage. Texas A & M University, College Station,
Texas. MM 4867-86-1, January 1986.
22. Green, A. E., and Zerna, W., Theoretical Elasticity. Clarendon Press, Oxford, 1968.
23. Wang, D. T., and Shearly, R. N., A review of solid propellant grain structural margin and
safety prediction methods. AIAA/ASME/SAE/ASEE 22nd Joint Propulsion Conference.
AIAA Paper No. 86-1415, 1986.
24. Bills, K. W., Jr., et a/., Non-linear fracture mechanics. Final Report. NWC-TP-5684.
February 1975.
25. Miner, M. A., Cumulative damage in fatigue. J. Appl. Mech ., Trans. ASME , Series £, 67,
1945.
26. Liu, C. T., Crack growth behavior in composite propellant with strain gradient. AIAA/
ASM E/S AE 20th Joint Propulsion Conference, June 1984.
27. Parr, C. H., End effect due to shrinkage in solid propellant grains. Bulletin of the 20th JAN -
AF Panel on Physical Properties of Solid Propellants , Vol. 1, November 1961.
28. Bills, K. W., Jr et al ., A cumulative damage concept for propellant-liner bonds in solid
rocket motors. J. Spacecraft , 3, 3, 1966.
29. ICRPG, Solid Propellant Mechanical Behavior Manual , CPI A Publications, 1963.
30. Thepenier, J., Gondouin, B., and Menez-Coutenceau, H., Reliability of solid propellant
grains: mechanical analog motor design and testing. AIAA/SAE/ASME/ASEE 23rd Joint
Propulsion Conference, AIAA-87, 1987.
31. Stankiewicz, F., Humbert, P. and Boule, P., Effect of dynamic loading on fracture
behavior of filled polymers. Impact Loading and Dynamic Behavior of Materials. DGM
Information Gesellschaft Verlag, Vol. 1, 1988.
32. Quidot, M., Dynamic fragmentation of compact energetic materials. Impact Loading and
Dynamic Behavior of Materials. DGM Information Gesellschaft Verlag, Vol. 2, 1988.
33. Mechanical Properties at High Rates of Strain, Conference, Oxford, edited by J. Harding,
March 1979.
34. Racimor, P. and Nottin, J. P., Mechanical behavior of solid propellants during tensile test
with variable temperature. AIAA/ASME/SAE/ASEE, 25th Joint Propulsion Conference No.
89-2645.
CHAPTER 7
Safety Characteristics of Solid
Propellants and Hazards of
Solid Rocket Motors
JACQUES BRUNET*
1. Introduction
The rapid growth of performance requirements and the new missions now
performed necessitate:
• the use of increasingly larger rocket motors;
• the use of, and search for, increasingly powerful propellants, or propel-
lants with increasingly faster combustion rates;
as well as finding propellants that remain very energetic while presenting a
lower level of vulnerability.
Because of these trends, and of the evolution of safety regulations, it is now
necessary to take safety issues into account at the beginning of any project.
2. Overview of Solid Propellant Rocket Motor
Hazards
During the course of their entire life cycle, from production to utilization,
solid propellant rocket motors can be found in many varied environments,
and subjected to stresses corresponding to a series of various activities.
Safety, under these conditions, is not only a function of the rocket motor per
se , but of the environment in which the rocket motor finds itself.
During the life of the motor, various undesirable events are likely to occur:
* With the participation of Michel VIDAL.
303
304
Jacques Brunet
• propulsion caused by untimely ignition: untimely operation;
• inadvertent initiation, with thermal and mechanical effects:
— explosion, with thermal, blast and projection effects;
— detonation of the propellant grain, with blast and projection effects;
• faulty performance, that may also result in the undesirable events listed
above.
These events are linked to the energy stored inside the propellant, and cause
the following physical effects:
• thermal fluxes;
• active or inert projections, which can be characterized in terms of density,
kinetic energy, and caloric energy:
— propulsion,
— projection of inert materials (fragments),
— projection of energetic materials (propellants);
• blast, accompanying:
— the mechanical explosion,
— the detonation of a portion of the motor or the entire motor.
These are the primary threats from the solid propellant rocket motors; but,
beyond these primary hazards, any active projection may lead to a secondary
hazard (other than kinetic or calorific) caused by the impact of energetic
material against walls or other objects against a wall.
In the case of a violent event, the blast causes an overpressure in the
surroundings, which may remain modest in the case of an explosion (several
kPa), or become very important (several MPa) in the case of a detonation.
3. Pyrotechnic Behavior of Solid Propellants
The pyrotechnic behavior of solid propellants can be characterized by:
• an evaluation of their various modes of decomposition;
• a knowledge of their reactions (threshold of reaction and type of reaction)
when exposed to certain types of stimuli.
A full knowledge of the solid propellant behavior is very valuable because it
allows us to:
• identify the modes of decomposition;
• know the level of stimuli that will cause a pyrotechnic reaction;
• compare the solid propellants with each other, and assess the general
behavior of a solid propellant grain or of a rocket motor by comparing it
against a reference solid propellant grain or rocket motor for which the
behavior is well known, and based, in particular, on past experience.
Safety Characteristics
305
3.1. DECOMPOSITION MODES OF SOLID PROPELLANTS
Propellants may, like any other explosive substance, exhibit various modes
of decomposition.
3 . 7 . 7 . Definition of the modes of decomposition
The major modes of decomposition are as follows:
• conductive combustion;
• convective combustion;
• detonation;
• thermal explosion.
Let us examine the propagation of decomposition into a solid propellant
(Fig. 1). The “reaction zone” is the zone existing at any time between zone
I — the propellant in its initial physical state, and zone II — the products of
the decomposition.
• When the reaction zone travels inside the initial matter (zone I), through
thermal conduction, we say that there is “deflagration.”
In that case, volume, pressure, temperature and material velocity vary in a
continuous manner from zone I to zone II inside of the reaction zone. The
propagation velocity is lower than the sound velocity in the solid propellant
and is called “deflagration velocity” (often called “the burning rate” of the
propellant). Solid propellants deflagrate in a linear “cigarette burning” mode
with slow propagation velocities up to high pressures.
• This steady propagation of the deflagration front into the unreacted solid
propellant is often called conductive combustion. The propagation
ZONE II
DECOMPOSITION
PRODUCTS
ZONE I
SOLID PROPELLANT
IN ITS INITIAL STATE
t
REACTION ZONE
DIRECTION OF THE PROPAGATION OF THE REACTION
Fig. 7.1. Sketch of the propagation of the decomposition in a solid propellant.
306
Jacques Brunet
velocities (burn rates) are in the range of several to tens of centimeters per
second.
• When the reaction zone travels through the unreacted propellant (zone I)
via a shock wave, we say that there is “detonation.”
Across this detonation wave, the volume, the pressure and the material
velocity of the matter experience a discontinuity. The typical propagation
velocity of a detonation ranges between 2000 and 9000 m/s. The detonation is
the functional decomposition mode of explosives. It is one of the accidental
and feared decomposition modes for propellants.
• The term “convective combustion” is often used in the case of porous
materials (a gunpowder layer, for example). In this case the reaction zone
travels via the penetration of heated gases in the spaces existing between
the grains. The propagation rates are in the 100-1000 cm/s range, and
because of the increased burning area and subsequent compaction of the
porous bed and accelerating pressure can lead to a deflagration to
detonation transition (DDT).
• The thermal explosion (cook-off), as described by Frank Kamenetski [2],
is a violent and somewhat peculiar reaction: it indicates a chemical
decomposition in the core of the matter.
Let us consider a chemical system, likely to react to thermal stress, which is
placed in a heated chamber at constant temperature T c (Fig. 2).
There may be a critical temperature T m such that:
• if T e < T m : then the heat produced per unit of time is lower or equal to the
heat dissipated: Q 1 < Q 2 . In this instance the state is steady and there is
no self-heating inside the system;
• if T e > T m : then the heat produced is greater than the heat dissipated per
unit of time: <2i > 62 - Here the condition is unsteady. Because the heat
Where Tj = Initial temperature of system, such as T «T e
Qi = Heat resulting from the reaction per unit of time inside the system
Q2 = Heat dissipated by the system per unit of time toward the outside.
Fig. 7.2. Sketch of a chemical system subjected to constant thermal stimuli T .
Safety Characteristics 307
produced cannot escape, the substance self-heats and can ignite, explode
and eventually even detonate.
The closer the temperature T e is to T m , the greater the likelihood for the
reaction to occur within the bulk of the propellant. It is in the vicinity of T m
that the “thermal explosion” phenomenon occurs.
3.1.2. Main characteristics of solid propellant
decomposition
3. 1.2.1. Combustion
Conductive combustion occurs, in solid propellants, in a very broad range
of pressures (1 Pa to 1000 MPa). Studies have particularly concentrated on
operational pressures, i.e. of the order of several MPa. Safety studies,
however, are also interested in the other pressures regimes (“ambient”
pressure and high pressures). The major methods used to characterize the
combustion of propellants are as follows:
• determination of the regression rate, measured at atmospheric pressure
on solid propellant grains;
• determination of burning rate versus pressure, using the classic “strand
burner” method (a small amount of propellant in a large vessel to give
essentially a constant-volume, constant-pressure burn. Each run deter-
mines the burn rate at a given pressure and many runs are required to
give the burn rate pressure curve);
• combustion under high pressure that might represent situations of high
level of confinement. This test is performed in a closed bomb with a static
resistance to rupture in the area of 1000 MPa. (A larger amount of
propellant is burned in the closed vessel giving a varied pressure-time
history. Reduction of the pressure-time curve gives a range of burn rates
versus pressure from one run.)
Figure 3 and Table 1 provide some samples of measurement results.
Table 1 Burning rate versus the pressure range in mm Is
Solid
propellant type
Pressure
Atmospheric
7 MPa
100 MPa
400 MPa
Classic butalane*
1.6
10
/
/
Butalane, high burning rate
3 to 8
20 to 80
/
/
Butalane with HMX
1.5
13
108
356
Double-base
0.5 to 1
7
66
334
High energy
0.5 to 1.5
8 to 30
/
/
* Aluminized polybutadiene composite propellant.
308
Jacques Brunet
p(MPa)
Fig. 7.3. Burning rate versus the pressure of typical propellants.
The monotonic character of these curves indicates that there is no
abnormal burning (burning into cracks, or sample deconsolidation). In some
instances, with certain high explosives, abnormal combustion occurs. This
abnormal combustion may lead to convective combustion and in the extreme
to deflagration to detonation transition.
3 . 1 .2.2. Detonation
(a) Detonation in the classical sense of the term
The main detonation properties of propellants are characterized by:
• the detonation critical diameter;
• the pressure required to initiate a given diameter of propellant often
measured by various gap tests;
• the TNT equivalency in terms of the blast effect.
Detonation critical diameter. The critical diameter is that diameter below
which a steady-state detonation induced by a violent plane shock wave is no
longer able to propagate. That is, the shock wave “dies out.” In explosives
Safety Characteristics
309
this happens in a relatively sharp manner. For example if a cone of explosive
is initiated at the base, the detonation will propagate toward the apex of the
cone until the critical diameter is reached, at which point the detonation will
die out. The stepped cylinder method (cylinders with decreasing diameter) is
often used (see Fig. 4). In this test the diameter where the detonation stops is
recorded by reading the witness lead plate. This diameter is called the
detonation critical diameter.
Card gap test . This test consists of determining how many cards, made of
cellulose acetate stacked to form a barrier, are necessary to prohibit the
transmission of the detonation from the donor explosive (320 g) to the
confined acceptor sample. The setup for this test is shown in Fig. 5.
Shockwave generator Substance
plate
Fig. 7.4. Determination of the detonation critical diameter; SNPE test no. 10.
Detonator
Booster
D = 40 mm
L = 160 mm RDX/WAX 95/5
M = 320 g.
Cellulose acetate cards
(thickness of each card =
0.1 9mm)
Sample of the materia!
to be tested
Witness booster
D = 40 mm
L = 40 mm H MX/WAX 95/5
M = 80 g.
Witness steel plate
Fig. 7.5. French card gap test.
310 Jacques Brunet
Table 2 De tonic characteristics of solid propellants
Propellant type
Critical
diameter
(mm)
CGT
(number of cards)
TNT equivalency
in blast effect
“Classic” composites
from 80 to 1000 a
<1
1.4
Butalane with HMX
from some mm to 100 mm b
from < 1 to 105 b
1.4
Double-base
2 to 25
from 55 to 100
1.2
High energy
2 to 10
from 100 to 200
1.4 to 1.7
a Function of the solid loading ratio.
b Function of the ratio and quality of the HMX.
TNT equivalency in terms of the blast effect. This is the ratio of the TNT
and propellant weight having the same effect at the same distances. Typical
results are shown in Table 2.
We discover that the detonation characteristics of propellants are as varied
as the formulas are different, but that the blast effect is about the same
magnitude.
(b) New mechanisms for transition to detonation
We saw that the transition between deflagration and detonation caused by
convective combustion cannot happen in an undamaged propellant grain
with correct mechanical properties.
Nevertheless, several detonations occurred in the 1970s in the United
States, during the development of the Trident missile [3-6]. It became
necessary to explain these accidents, to imagine other mechanisms. Figure 6
presents, as a scheme, this new approach.
This scenario, which includes damage of the solid propellant leading to the
creation of convective combustion conditions, reveals, on one hand, that
correct design of the rocket motor is a key to operational safety, and on the
other hand, that this DDT process can be eliminated by using propellant with
a low propensity to fine fragmentation, therefore with good mechanical
properties.
The most common test used to characterize the propensity of the propel-
lant to this type of failure is the “friability or toughness” test, also known as
the “shotgun” test. This consists of determining the condition of a piece of
propellant grain fragmented through impact against a plane wall, by burning
it in a closed bomb. The test principle is illustrated in Fig. 7.
The derivatives of the maximum pressure obtained on fragments of
propellant grains, after impact, are recorded for each manometric chamber
Safety Characteristics
311
Fig. 7.6. Scenario of the DDT transition of a propellant grain.
test. These tests permit to plot the curve:
= / (impact velocity)
This curve is useful because ancillary experiments showed that when the
propellant was damaged sufficiently to give 18 MPa/ms in the 90 cm 3 closed
bomb, it was sufficiently damaged to produce DDT in a DDT tube
experiment. Thus the impact velocity that causes damage sufficient to
produce this 18 MPa/ms dp/dt in the 90 cm 3 closed bomb, is called the
critical impact velocity or CIV. Values of CIV of 200 m/s are considered
good, that is a tough propellant which is not very friable, while 100 m/s is
indicative of poor, friable propellant.
These accidents have led to the analysis of the failure mode of the firing
operation. The experiments carried out revealed, in particular, the so-called
“XDT” phenomenon (delayed detonation through shock). J. F. Kincaid [7]
has put together a study combining all of these tests and their results.
The delayed detonation occurs at a time later than the normal transit time
of the shock through the material. These reactions not only occur at times
312
Jacques Brunet
Fig. 7.8. NOL card gap test results showing SDT and XDT (from ref. [8]).
longer than characteristic of SDT, they also require a lower stimulus, for
example an increased number of cards in the card gap test as shown in Fig. 8.
Sample size and mechanical properties also determine the initiation
threshold as seen in Fig. 9.
So, detonation initiation by shock can be resumed in the following manner:
• high shock -► SDT 1 D initiation;
• low shock -► XDT 2 D and 3 D initiations.
Safety Characteristics
313
0.7,
0 . 6 ^
| 0.5
§0.4h
uj 0.3
DC
X
0 . 2 -
0 . 1 -
0
o A
20 40 60 80 100 120 140 160
SAMPLE DIAMETER (mm)
Fig. 7.9. Dependence of the velocity threshold for observation of XDT on sample
diameter for various propellants A through E (from ref. [9]).
3.2. SENSITIVITY OF PROPELLANTS TO VARIOUS STIMULI
3.2. 1. Impact sensitivity
Traditionally, at SNPE the Julius Peters drop-hammer test was used to
determine the sensitivity to impact of high explosives. Initially, it was also
used for solid propellants. Its major drawback is the very small quantity of
Fig. 7.10. Sensitivity test with a 30 kg fall-hammer; SNPE test no. 17.
314
Jacques Brunet
material that is used to perform the test: 20 mm 3 . The “30 kg fall-hammer
test” is now preferred; its major advantage resides in the capability of testing
100 g of material.
This test is, in addition, very interesting because it allows us to make a
distinction between the types of reaction of the explosive substance:
• violent reaction with propagation (detonation);
• local reaction or ignition.
Generally, there is no propagation of violent reaction in the specimen of any
solid propellants, up to an impact stimulus from 4 m high. However, local
reactions, ignitions with or without propagation are observed.
3.2.2 . Sensitivity to friction
As for the impact sensitivity testing discussed above, the sensitivity to
friction test is carried out with the Julius Peters testing device. The principle
of this device is illustrated in Fig. 11. It allows classification of the friction
sensitivity of the solid propellants, but the safety margin in relation to the
stimuli cannot be determined. Typical results obtained are given in Table 3.
To determine the safety margin of an operation performed on the solid
propellant, this test can be complemented by other selective tests. These
consist of rubbing propellant specimens, weighing several grams on surfaces
(F max = 353 newtons)
Fig. 7.11. Device for the friction sensitivity test “Julius Peters”— SNPE test no. 16.
Table 3 Sensitivity to friction of solid propellants
Composite 80 to 150 N
Composite with burning rate modifier 50 to 90 N
Double-base and high energy without ammonium perchlorate 50 to 353 N
Ammonium perchlorate high energy 60 to 150 N
Safety Characteristics
315
Pressure (MPa)
Fig. 7.12. Results of linear friction tests; SNPE test no. 76.
selected according to the data required, for periods of time lasting eventually
up to several tens of seconds. By performing a series of tests a curve can be
plotted from which safety margins can be obtained for pyrotechnic events
considered as likely to occur during an operation inducing this type of stress.
Figures 12 and 13 provide examples of such curves.
The solid propellant itself can be a surface that is selected, in which case an
increase in sensitivity was noticed when moving from a steel surface to a
propellant surface.
c
LU
_1 I
10 10 2
Time (s)
Fig. 7.13. Results of rotary friction.
316
Jacques Brunet
Steel plate
e » 10 mm Substance to be tested
60 mm
Point of impact of the
ordinary 7.5 caliber bullet
Steel box 0,4mm thick
60 mm
Fig. 7.14. Sensitivity to 7.5 mm caliber bullet impact; SNPE test no. 32.
3.2.3 . Sensitivity to projectiles and fragments
It is, in fact, the sensitivity to impact from bullets that is usually
determined. A test currently performed is shown in Fig. 14.
Generally, the results obtained at ambient temperature are as follows:
• ignition in all solid propellants;
• no violent reaction up to impact velocity of 930 m/s.
This systematic ignition, which we see in all composite propellants regardless
of the velocity (beginning at 385 m/s), occurs in double-base propellants
beginning at 555 m/s.
In Nitrargols the ignition threshold velocity decreases when the ammo-
nium perchlorate content increases. These results have been confirmed by
tests performed with rocket motors.
Nevertheless for rocket motors using solid propellant with small critical
diameter of detonation we have to perform tests on more realistic models. In
fact it is necessary to take into account that the vulnerability of a rocket
motor is the vulnerability of a system. Some new results show that detonation
can be obtained essentially due to a bore effect [10].
In this work detonation occurred when the bullet passed through the
center bore in the motor, while detonation did not occur when the same
caliber bullet with the same velocity passed through just propellant web
(impact off-center so that the path of the projectile does not pass through the
bore).
3.2.4. Sensitivity to temperature increase
3.2.4. 1. Temperature of ignition
The ignition temperature of a solid propellant is the temperature at which
ignition of the solid propellant occurs when the temperature of a small-size
Safety Characteristics 317
specimen is raised; it is dependent only on the composition when the weight,
the shape and other aspects of the specimen are given.
This characteristic varies with the temperature gradient. Two tests are
commonly performed using 200 mg of shredded product:
• progressive heating with a standard gradient of 5°C/min;
• Sudden heating, which is achieved by plunging the product suddenly into
an environment at a specific temperature. The ignition temperature is the
temperature at which the propellant ignites within 5 s.
3. 2.4.2. Temperature of thermoinitiation of an unconfined
solid specimen
In the preceding sections we gave a brief description of the thermal
explosion phenomenon. This phenomenon is different from that of ignition.
A composite propellant with ammonium perchlorate that does not contain
any burning rate modifier, for example, can react very violently at a
temperature of 175°C after several hours. This is the case of an accelerated
chemical reaction at the core of the sample. A summary of the situation is
given in Fig. 15.
The sensitivity to thermal explosion is determined through the cook-off
test. The principle of this test is given in Fig. 16.
The specimen is contained in a cylinder made of steel or aluminum. The
results of this test can be influenced by the environment and the size of the
specimen [11]. The results obtained from progressive heating and thermoini-
tiation tests are indicated in Table 4.
Whenever we have seen the thermal explosion phenomenon occur, it
always is within a narrow range of temperatures (approximately 10°C).
Nitrargols G containing ammonium perchlorate have no temperature
Temperature (°C)
Time (s)
Fig. 7.15. Diagram of the evolution of the reaction temperature versus time.
318 Jacques Brunet
Temperature probes
Table 4 Experimental results from thermal stimuli
Results
Ignition
temperature
(progressive heating)
Cook-off — 0 50 mm, h 50 mm
(at constant temperature)
Propellants
Result
Maximum
pyrotechnic event
“Classic” composites
270 to 320
Approx. 175°C
Thermal explosion
High burning
rate composites
280 to 170
Decreases until
120°C when the
catalyst ratio
increases
Same
Epictete (CDB)
165 to 185
100 - 110°C
Same
Nitrargols
(high-energy propellant)
without perchlorate
with perchlorate
160 to 180
170 to 180
110- 110°C
No critical values
Same
Ignition
limits or cook-off phenomenon. Decomposition occurs through burning. Test
results that are now available demonstrate that their decomposition is
directly controlled by the consumption of the nitric ester stabilizers of the
formulation. The reaction temperature is independent of the size of the
specimen.
3. 2.4. 3. Fast cook-off and slow cook-off
These terms describe thermal stimuli observed, typically, in munitions in
an operating environment.
Safety Characteristics 319
• Fast cook-off corresponds to a munition exposed to an intense and direct
fire. The munition is engulfed within the flames.
• Slow cook-off corresponds to a munition subjected to a relatively low
heat flux. Under these conditions it is understandable that the tempera-
ture of the munition increases very slowly.
The tests discussed in Sections 3.2.4. 1. and 3. 2.4.2. can also be used to study
this type of slower thermal stimulus.
3.2.5 . Sensitivity to static electricity
3.2.5. 1. Background
Until 1975, France, like most other countries, performed a test using
around 100 mg of propellant to determine its electrostatic sensitivity. This
test is comparable to the Picatinny Arsenal test [12] and is shown in Fig. 17.
In this test, propellants in the shape of compact discs were always found
insensitive. Occasionally, after some tests, the propellant discs were found to
have a very small axial hole.
3.2.5 2. Recommended operational method for the tests
During the 1970s, ignitions of composite propellant grains occurred in
manufacturing facilities. Investigations demonstrated that these ignitions
could only have been caused by static electricity.
Additional tests were then performed, leading to the adoption of a new
testing method that proved to be more representative of the accidents that
had occurred [13]. The principle of this new method is shown in Fig. 18.
Using a pointed electrode, the propellant grain (0 = 90 mm, height =
100 mm) is subjected to the discharge measuring 34.7 nF, charged at 30 kV.
Thirty successive discharges are released into the grain. The result is
considered as negative when there are no cracks and no ignition. A
composition is declared electrostatic-insensitive when negative results have
320
Jacques Brunet
30MH
been obtained on three grains of that propellant composition, at the specific
temperature. Further details can be found in the chapter on composite
propellants (Chapter 10).
4. Assessment of the Risks Presented by
Propellant Grains
A risk assessment consists of assigning a probability of occurrence to each
potential hazard, for each phase of the life of propellant grain. There are two
traditional methods used;
• the regulatory approach;
• the analytical study.
4.1. THE REGULATORY APPROACH
4. 7. 7. Major regulations
The propellant industry is subject to the application of various regulations.
The most general in its scope of these regulations is the UN Recommenda-
tion [15].
Generally speaking, these regulations establish hazard categories or sec-
tions for the various explosive substances, solid propellants in this case,
corresponding for the most part to the pyrotechnic effects likely to be
encountered.
Table 5 provides, for example, the definitions of the hazards divisions of the
French Labor Regulation (almost the same definition as UN).
They also provide data for a decision chart, based on tests or experiments
whose results have been quantified and compared with criteria or sanctions
Safety Characteristics
Table 5 Classification of hazards of explosive substances and objects
321
Class Division Characteristics of the substances
number number or articles in this section
1
1 Substances or articles essentially involving a mass
explosion hazard, i.e. affecting almost the entire load
virtually instantaneously.
2 Substances or articles involving a projection hazard
but no mass explosion hazard.
3 Substances or articles involving a fire hazard with a
minor blast or projection hazard, and no mass
explosion hazard.
This division includes the following two subdivisions:
Subdivision 3a, consisting of substances or articles
whose combustion gives rise to considerable radiant
heat;
Subdivision 3b, consisting of substances or articles
that burn fairly slowly, or burning one after the
other with minor blast and projection effects.
4 Substances or articles involving no significant hazard,
designed or packed so as to exhibit only relatively
minor hazard or whose effects, in case of ignition or
initiation, do not give rise to the projection of
fragments of appreciable size, and remain in any case
small enough not to significantly hinder fire-fighting
operations and the application of emergency measures.
5 Substances that are, when they explode, as hazardous
as those of Section 1, but that are relatively insensitive.
These substances display a very low probability of
initiation and transition from combustion to
detonation except when in large amounts in a small
and confined space. They may not explode when
exposed to outside fire.
allowing the classification of the product into one or another of the hazards
divisions defined in Table 5.
Finally, they provide a general definition of the dispositions, precautions
and facility designs for the established classes of products.
National or international regulations on transport, storage, possession,
and use of hazardous substances are being or have been revised in accordance
with the UN recommendations.
The differences existing between the procedures are explained by the fact
that these regulations take implicitly into account the probability of the
occurrence of a stimulus. It is therefore understandable, for instance, that
stimuli considered in the case of storage are different from those in the case of
transport.
322
Jacques Brunet
The only regulation that explicitly considers the probability of the occur-
rence of pyrotechnic events is the French Labor Regulation [16].
The test most widely used for all regulations is the card gap test. There are,
however, various versions of this test, and the criteria followed by the various
regulations differ, possibly resulting in making comparisons difficult. The test
used in France and related results are described in Section 2. The determina-
tion of whether a product should be upgraded from Hazard Division 1.3 to
1.1 is based on card gap tests greater than 240 French cards in France and 70
American cards in the United States, the latter being equivalent to approxi-
mately 95 French cards, because the thickness of the cards is different. The
positions on this criterion seem to be very far apart. It would be necessary,
however, in order to judge the validity of either regulation, to compare them
in their entirety and not on that particular point only.
4. 1.2 . Labor regulations
The assessment of threats and the corresponding assignment to a hazard
class in accordance to French labor regulations is particularly applicable to
small propellant grains rather than large grains for various reasons, including
the significant number of specimens required (i.e. cost and space limitations).
The assignment to a hazard class is done based on a procedure which
includes a series of tests, and is applied to new explosive substances or articles
(such as free-standing grains, rocket motors, and others).
The procedure involves five steps:
The first step involved in this classification consists of determining whether
the rocket motor or the propellant grain is a new type or “insufficiently
known”.
Of course, when the design of the rocket motor, or the propellant grains,
shapes or compositions, is in fact very new, it is ipso facto insufficiently
known. But this case is a very rare one, and what is termed as new is the
result, in practice, of more or less extensive modifications to existing, known
propellant grains.
In practice, to be able to avoid having to perform all required tests, it is
necessary to provide proofs that a new propellant or motor can be placed in
the same category as existing propellants or motors.
These studies and analyses, which make up the first step of the procedure,
can be summarized as follows:
• acquire the technical elements of the definition of the type of propellant
grain or motor under consideration;
• identify the differences;
• analyze these differences;
• conclude whether the analogy is reasonable — if it is not, proceed to the
second step.
Safety Characteristics
323
Fig. 7.19. Procedure to include propellant grains in hazards divisions— right part of
the decision flow-chart.
When in doubt, the higher hazard class is selected, as described above.
Tailoring of the procedure to the case of propellant grains is discussed below.
The beginning of the path is shown by the thicker line in Fig. 19, within a
general decision flow-chart.
The second difficulty involved in the classification, based on the flow-chart,
is coming to a conclusion about the meaning of the word “confinement.”
Consequently, the second step consists of qualifying the confinement of a
propellant grain.
One possible method is:
The “decision chart” indicates that the substances in bulk, or loosely
packed (i.e. in a cardboard box, or a thin wood box) are considered to be “not
confined,” or “in an object that provides no confinement”.
This confinement concept aims essentially at ensuring that the risks of
transition from deflagration to detonation are taken into account. Further-
more, we know that a propellant will not transit to detonation unless it has
been previously finely fragmented after, for example, an early-damaged
material.
As long as the constituent material of the grain is undamaged and solid, the
propellant grain itself becomes in some ways like an open container. We are
able, then, to consider that the confinement is tied only to the Klemmung of
the propellant grain and to the probable effects of the bursting of the motor,
whether it acts as a container under pressure or it is case-confined in the case
of accidental burning. A technical equivalence of the confinement concept
may then be suggested for the rocket motor.
The technical equivalence of the definition for the expected confinement is
specific to the particular object that a solid propellant motor constitutes.
When the four following conditions are satisfied simultaneously, it is said
that there is no confinement.
324
Jacques Brunet
• First condition. This concerns the propellant constituting the solid pro-
pellant grain.
This propellant must burn in a normal layerwise manner up to very
high pressure levels.
• Second condition. This requirement is related to the violence of the
eventual bursting of the container under pressure, which is the propellant
grain itself in the case of accidental burning.
Precise specifications related to the characteristics of the propellant
and its case are used to determine these two conditions.
• Third condition. The propellant grain is loosely packaged, or not at all
(absence of confinement from packaging).
• Fourth condition. The storage condition of a number of rocket motors
does not create any significant additional confinement (absence of
confinement in storage).
When all four conditions are satisfied we may say that there is no confine-
ment and the left portion of the decision chart is used. If even one of these
conditions is not satisfied, the right side of the decision chart is used.
The following steps consist of characterizing the situation and following
the applicable procedure for classification.
Finally, the fifth and last step consists of ensuring that the quality
assurance of the program guarantees that each propellant grain or rocket
motor will have the same characteristics of the specimens used to perform the
classification tests.
4.2. ANALYTICAL ASSESSMENT
This method is much more general and complete than the preceding one
[17]. It is better suited for large rocket motors.
Three steps are involved:
The first step consists of preparing an exhaustive list of all possible stimuli.
By stimuli, we mean both a stimulus proper, i.e. coming from the outside, and
possible failures of the system, in particular, a defective operation. The list
created must show, for each stimulus:
• the probability of the stimulus;
• the gravity of the stimulus (such as among other things, intensity and
duration).
The second step consists of creating a general scenario of the behavior of the
rocket motors under the various stimuli identified in the first step. A typical
scenario is shown in Fig. 20. The goal of this type of scenario is to assess the
Safety Characteristics
325
Fig. 7.20. General scenario of the behavior of a rocket motor faced with a threat.
explosive hazards and to discover eventual degradations and their conse-
quences.
The third step involves the analysis of the possible behavior of the rocket
motor for a specific stimulus. A sample of an analysis is given in Fig. 21, for
the case of a threat resulting from a shaped charge.
The result of this analysis is the probability of an undesirable pyrotechnic
event.
For the third step, the following are indispensable to be able to quantify the
probability:
• the performance of basic tests;
• the use of computer codes;
• the performance of tests on models.
For instance, the example in Fig. 21 requires, among other things:
• knowledge of the critical detonation diameter of the composition, which
is a basic test;
• determination of the fragmentation condition due to the stimuli, which
requires the use of a code.
326
Jacques Brunet
Fig. 7.21. Analysis of an attack by a shaped charge jet.
Bibliography
1. MfiDARD, L., Les Explosifs Occasionnels , vol. 1. Proprietes-Collection Technique et Docu-
mentation, 1978.
2. Kamenetsky, F., Diffusion and Heat Transfer in Chemical Kinetics . Translated from the
Russian edition by N. Thon. Princeton University Press, 1955.
Safety Characteristics
327
3. Panningthon, F., Man, T. and Pernom, B., Rocket Propulsion Hazard Summary : Safety
Classification, Handling Experience and Application to Space Shuttle Payload . May 1977.
4. Weiss, R. R., Vanderhyde, N. and Merrill, C., Review of USAF Treatment of Solid
Propellant Rocket Motor Hazards. AGARD Conference Proceedings No. 367, 1984.
5. Brunet, J. and Paulin, J. L., Etude de la transition de la deflagration a la detonation des
propergols prealablement fragments. AGARD Conference Proceedings No. 367, 1984.
6. Lee, E. L., James, E., Green, L., Von Holle, W. and Tarver, C., Lawrence Livermore
National Laboratory. Curran, D., Murri, W. and Seaman, D., Contributors. Stanford
Research International. Response of Propellants to High Dynamic Stresses. The Uses of Gun
Launch Techniques. AGARD Conference Proceedings No. 367, 1984.
7. Kincaid, J. F., The Determination of the Propensity for Detonation of High-Performance
Propellants. ICT Jahrestagung, pp. 155-168. Karlsruhe, Germany, 1982.
8. Keefe, R. L., Delayed Detonation in Card Gap Tests— 7th Symposium on Detonation, pp. 233,
240, 1981.
9. Blommer, E. J., Delayed Detonation of Propellants in the 25 mm Instrumented Shotgun
Test—J9th JANNAF Combustion Meeting, vol. II, pp. 225-246, 1982.
10. Nouguez, B., Berger, H., Gondouin, B. and Brunet, J., An Odd Bore Effect on Bullet
Induced Detonation of High Energy Propellant Grains. ADPA symposium, 23-25 October
1989, Virginia Beach.
11. Kent, R. and Rat, M., Explosion thermique (cook-off) des propergols solides. Propellants
and Explosives ,1, 129-136, 1982.
12. Westgate, C. R., Pollock, B. D. and Kirshenbaum, M. R., Electrostatic Sensitivity Testing
for Explosives. Technical Report 4319. Picatiny Arsenal, Dover, New Jersey, USA.
13. Kent, R. and Rat, M., Phenomenes d'electricite statique dans la fabrication et la manipulation
des propergols solides. ICT Jahrestagung, 423-438. Karlsruhe, Germany, 1981.
14. Kent, R. and Rat, M., Static Electricity Phenomena in the Manufacture and Handling of Solid
Propellants. 20th DDESB, Norfolk, Virginia, USA, 1982.
15. Recommandations relatives au transport des matieres dangereuses . Nations Unies ST/SG/
AC. 10/1 Rev. 5 and ST/SG/AC 10/11, 1988.
16. Securite pyrotechnique. Journal officiel de la Republique Fran^aise. 26 Rue Desaix 75727
Paris Cedex 15. No. 1196 ISBN 2 11.0702082.6, 1981.
17. Lievens, C., Securite des Systemes. Cepadues Editions, Toulouse, 1976.
CHAPTER 8
The Main Families and Use of
Solid Propellants
ALAIN DAVENAS
1. Background
The recent and spectacular development of rocket propellants is in sharp
contrast to the slow, even non-existent development of materials for propul-
sion purposes during previous centuries, when the single basic product, black
powder, was not sufficient to propel objects by gas jets, in spite of numerous
attempts. At the end of the 18th century the main application of this type of
propulsion was for entertainment purposes: fireworks. It was not until the
beginning of the 19th century that the military began again to take an interest
in rockets.
The great industrial growth of that period promoted their development,
and it is clear that the history of propulsion is closely linked to the history of
the chemical industry which, in a very short time, offered scientists possibili-
ties for research of new products. The 19th century saw the discovery of new
basic molecules, such as nitrocellulose and nitroglycerine, followed by much
research designed to master their usage as explosives as well as propellants.
The end of that century and the beginning of the 20th century witnessed the
emergence of the first modern propulsive powders, today’s double-base
extruded or cast propellants.
The development of propellants is not, however, linked solely to the
development of chemistry; ballistics development was a second essential
factor. For 150 years the experts doing research in these specific areas
judiciously combined their knowledge and efforts to make rocket propulsion
what it is today. In the course of time, other research areas were applied to
rocket propulsion: mechanics, thermodynamics, fluid mechanics and indus-
trial technologies, etc.
While the second half of the 19th century witnessed the beginning of the
development of today’s double-base propellants, known in France as “homo-
geneous propellants,” the second half of the 20th century was characterized
329
330 Alain Davenas
by the development of composite propellants containing aluminum and
ammonium perchlorate.
Here again, the development was linked to the progress made in chemistry,
and in particular to the development of plastic materials, which was very
rapid during the Second World War. From 1950 on, polyurethane chemistry
found in propellants an ideal area of application. This outlet continues to
appear the most significant in industrial terms, as emphasized by Klager [1].
But other systems had been researched before that, and some of their
applications are still in existence today, for example the polystyrene-poly-
esters and polysulfide systems [2], and polyvinyl chlorides [3]. These form-
ulations were developed by large companies, mostly American, who at the
time were interested in rocket propulsion. Polystyrene-polyesters, followed
by the polyurethanes, resulted from the activities of Aerojet General Corpo-
ration and General Tire and Rubber Company. The polysulfides, then
polydienic structure products, came from Thiokol Chemical Company and
the Jet Propulsion Laboratory. Atlantic Research Company was responsible
for PVCs, while Hercules was mostly interested in single and double-base
propellants and the possibilities of improving them [4]. Even though, during
the past 30 years, the activities of each of these various companies were
mainly a function of the sectors of applications they were assigned, they
continuously looked for ways to improve performance and link the qualities
and advantages of the two basic families. This slowly led to the creation of a
new third family of high-energy products, implemented following the typical
composite propellant methods, which are known today as composite double-
base propellants [4]. Both families were combined and gave birth to high-
performance products at the end of the 20th century. Figure 1 gives an
COMPOSITE PROPELLANTS
Asphalts
PVC-Polysulfides-Polyester styrene
Hydroxyl polymers
Polyether and
-*► polyester based
polyurethanes
Metallic additives
-*■ and bonding agents
!-*■ HTPB binder
Carboxyl polymers
PBAA binder
-► (acrylic acid
butadiene copolymer)
PBAN (acrylonitril,
-► acrylic acid,
butadiene copolymer)
CTPB binder
DOUBLE BASE PROPELLANTS
Extruded double-base (EDB)
I
Cast double-base (CDB)
I
Composite modified
cast double-base (CMDB)
\
High energy composites
crosslinked double-base (XLDB)
High energy
propellants
Fig. 8.1. Chronological development of double base propellants and composite
propellants.
Main Families and Use of Solid Propellants 331
overview of this evolution through the major improvements brought to the
various families of materials.
The development of solid propellants was also accompanied by the
development of insulation materials. The research on complementary proper-
ties in areas as varied as combustion control, thermal protection of struc-
tures, propellant case-bonding, signature, and mechanical behavior, has
required the involvement of all sectors of chemistry.
Simplified in the extreme, the development of research in the area of solid
propellants has led, as a result, to the existence of two separate major
families:
• double-base or homogeneous propellants;
• composite propellants.
Figure 2 provides a basic diagram of their formulation and manufacturing
processes.
For more information than is provided by this very quick historical
presentation, it will be useful to read the very interesting article published by
Lindner [5] in the Encyclopedia of Chemical Technology , and in French, the
work of Quinchon and Tranchant [6].
2. Utilization in the Propulsion Stages for
Missiles or Space Launchers
A color photograph in this book shows the range of industrial grains
manufactured by one propellant company, with the various families of
propellants grouped according to applications. For each specific application
TYPE
DOUBLE BASE
PROPELLANTS
USE
TACTICAL
MISSILES AND
VARIOUS
SYSTEMS
INGREDIENTS
NITROCELLULOSE
+
NITROGLYCERINE
NAME /PROCESS /APPLICATION / ]
EDB
EXTRUSION
FREE
STANDING
GRAINS
CDB, CMDB
CASTING
FREE-STANDING
|orCASE-BONDED|
GRAINS
TYPE
USE
INGREDIENTS
COMPOSITE
STRATEGIC
AND
AMMONIUM
AND
TACTICAL
PERCHLORATE
HIGH ENERGY
MISSILES.
+ BINDER
PROPELLANTS
SPACE
+ ALUMINIUM
BOOSTERS
/ NAME
Q|
ISORGOLS
BUTARGOLS
NITRARGOLS
G
(XLDB)
PREMIXING
+ MIXING
+ CASTING
i
FREE-STANDING
GRAINS or
CASE-BONDED
GRAINS
Fig. 8.2. Propellants: use-composition-process.
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Alain Davenas
the technical or industrial specifications dictated the selection of a particular
type of grain, through design work, as explained in Chapter 2. However,
general trends do emerge: high-mass grains are made with composite
propellants or composite double-base (CMDB) and are case-bonded and
those of very low mass are more often made of a homogeneous propellant or
smokeless CMDB or XLDB. So we can see that there are some general
principles and criteria that guided their selection.
We shall now look at the manner in which the various propellants respond
to the general requirements for the propulsion stages of a missile: require-
ments for performance, physical and mechanical characteristics, signature,
manufacturing processes, cost, safety, and vulnerability.
2.1. PERFORMANCE COMPARISON OF INDUSTRIAL
PROPELLANTS
2. 1. 7 . Energy performance
Figure 3 shows the two major energy characteristics of a propellant: the
standard specific impulse l \ m , and density p. Very roughly: the greater the
product p /* m , volumetric specific impulse, which we are using as the energy
index, the better-performing the family being investigated.
On the diagram are the family of “low signature” propellants within the
visible range, inside which the Nitramites (smokeless XLDB) perform better
than the classic homogeneous EDB and CDB and the family of aluminized
propellants with approximately 15% greater performance?
To the non-expert an energy difference of 15% might seem insignificant. In
real applications, however, its significance becomes much clearer. Take for
example a three-stage ballistic missile with a 10,000 km range and typical
range differential coefficient, indicated in Table 1 for stage I and II, carrying
respectively a 24.5 and 10 ton propellant grain. The related range increase
resulting from the higher performance of the first two stages will be 3370 km;
Table 1 Range differential coefficients for the first two stages of a three-stage missile with a
10,000 km range [7].
First stage
Second stage
dP
,'M p (km/kg)
0.4
0.5
dP
— (km/s)
40
70
Main Families and Use of Solid Propellants
333
Specific
Impulse
XLDB - Nitralane
HMX filled HTPB = Butalane X
HTPB = Butalane
PU = Isolane — SMOKY
XLDB = Nitramite G
CMDB = Nitramite E ZZZ REDUCED SMOKE
PU = Isolite
CDB = Epicete : MINIMUM SMOKE
EDB = SD
Fig. 8.3. Propellant characteristics p , Is.
i.e. a 40% range increase will be gained by this performance increase on all
three stages.
Consequently, whenever greater propulsion performance is the primary
goal, as is the case for long-range ballistic missiles, space launch boosters, and
apogee motors, aluminized composite propellants are preferable.
In the case of tactical missiles a trade-off must be found between perform-
ance and signature. It is a delicate trade-off. The search for a reduced
signature to prevent early detection of the missile without performance loss
has, of course, been the major factor behind the important research done on
the nitramite propellants (smokeless propellants based on a nitramine and
energetic, nitroplasticized, binder). This criterion might in the future play an
334
Alain Davenas
increasing role also for ballistic missiles, with the objective of decreasing the
possibility of detecting and destroying these missiles.
2.1.2. Burning rate characteristics
Limitation of propellant burning rates available for a specific project is one
of the most frustrating difficulties for the designer who would prefer the use of
the greatest possible range of burning rates.
Figure 4 shows the burning rate range, at a given pressure of 7 MPa for the
most commonly used propellants. When seeking the highest burning rates the
answer lies with composite propellants for the usual burning times for missile
propulsion stages (several seconds to several tens of seconds). However, for
very short burning times, on the order of a few tens of milliseconds, which are
often used for light anti-tank missiles where a low signature is generally
required, EDB (extruded double-base) propellants (solventless) are a prime
XLDB = Nitralane
HMX filled HTPB = Butalane X
HTPB = Butalane
HV - HTPB = Butalane HV
HV - HTPB / CTPB = Butalites HV
XLDB = Nitramite G
CMDB = Nitramite E
CDB = Epictete
EDB = SD
HV = High Velocity
Fig. 8.4. Propellant characteristics.
Main Families and Use of Solid Propellants 335
solution because of their physical properties lending themselves particularly
well to designs with thin webs (fraction of a millimeter).
For very long burning times, solutions can be found in every family,
although they are always accompanied by a significant decrease in the energy
characteristics.
“Average” burning rate ranges can be obtained with every type of
propellant. It is useful to know, however, that EDB propellants offer greater
burning rates than the CDBs for an equal level of energy. This is a
characteristic inherent in the product (Chapter 9). And again, in applications
where a large range of operating temperatures is required, the lower
temperature coefficient of the homogeneous propellants may compensate for
low rates of specific impulse per unit volume. As a matter of fact, with an
identical burning time at 20°C, the propellant with the highest temperature
coefficient results in a higher maximum working pressure of the grain at high
temperatures, necessitating a thicker structure for the motor, resulting in a
weight increase. Similarly, the decreased flow rate at low temperatures can
have negative effects because of the resultant reduction in thrust.
2. 1.3. Ducted rocket or ramrockets
Based on energy performance, the choice between a conventional propel-
lant engine or a ramrocket appears obvious for a tactical missile. But taking
into consideration the overall constraints, that choice is no longer as clear, as
is demonstrated by the relatively limited number of modern applications
(missiles with integrated boosters) in existence today: the Soviet SAM 6 and
the French ASMP* with liquid ramjet. But there are some cases where the
advantages are obvious [8], as demonstrated in Fig. 5 by a plot of the weight
Air, Sol, Moyenne Portee: air-to-ground medium range.
336 Alain Davenas
of a missile for a zero-altitude mission with a 100 km range, as a function of
the cruising Mach number.
2.2. COMPARISON OF PHYSICAL AND MECHANICAL
CHARACTERISTICS
These characteristics very often dictate the feasibility of a given architec-
ture, directly influencing performance (volumetric loading ratio, evolution of
grain burning surface versus time) and cost.
2.2.1. Mechanical behavior
The mechanical properties of solid propellants are given by the master
curves of the parameters S m , e m , £ tg , and e, which are explained in Chapter 6
and illustrated in Fig. 6.
These curves reveal three distinctive zones, each related to a specific
behavior of the material:
• the glassy zone (Zone 1), characterized by a constant modulus in the
short time range, indicating a fragile linear elastic behavior;
• the transition zone (Zone 2), in the interim time range, emphasizing the
viscoelasticity of the material;
• the rubber-like zone (Zone 3), in the long time range, with stable behavior
of the propellant, which can be represented by a law of the type:
E r (t/a T ) = E(t/a T y n
Fig. 8.6. Mechanical behavior of solid propellants.
Main Families and Use of Solid Propellants 337
These three zones are found in all propellant families:
• CDB and CMDB;
• XLDB;
• composites with polyurethane and polybutadiene (HTPB and CTPB)
binders.
This allows us to define the following specific parameters:
• width of the transition zone;
• glassy modulus;
• rubber-like modulus.
Width of the transition zone
The transition zone is the zone where the propellant’s viscous mechanisms
are activated.
The width of the glass transition zone attests to the variety of viscous
mechanisms that can be activated. Typical values are given in Table 2, for the
various materials.
The glass transition zone of composites and XLDB is reached during load
times that are shorter than the usual pressurization times at low temperature.
These propellants are therefore very rarely stressed in the glass states.
All propellants show a relatively stable behavior, significant strain at
rupture, and a time of relaxation under constant load stress/strain for
equivalent times greater than 10 5 min, which corresponds to long-term
storage (over 1 year).
Glassy modulus-rubbery modulus
The glassy transition zone is characterized by the values of the elasticity
modulus.
The behavior for long times specific to each propellant can be represented
by the following type of equation:
E {£) =E (iY
It is therefore impossible to establish a rubber-like modulus as described for
classic linear viscoelastic materials ( E = constant). For comparison purposes
Table 2 Width of the glass transition zones of the main propellants
Propellant
EDB CDB PU HTPB CTPB XLDB
t y to t 2 (in mn) 10 “ 4 to 10 s 10' 6 to 10° 10“ 12 tol0° 10“ 8 to 10° 10 9 to 10 2 10“ I4 tol0 2
Width (tens of mn) 8 5 11 7 10 11
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Alain Davenas
Table 3 Relaxation modulus of propellants for long-term storage
Propellant
EDB
CDB
PU
CTPB
HTPB
XLDB
£ glass (MPa)
2000
1000
3000
300
200
2000
Eoo(10 7 ) (MPa)
3
1.5
2
0.7
0.5
1.5
between the various propellant families, the modulus at t/a r = 10 7 min is
used in Table 3.
The family of propellants we are looking at shows two types of behavior:
• high glassy modulus materials: EDB, CDB, PU, XLDB;
• low glassy modulus materials: CTPB and HTPB composites.
In addition, the transition is much more pronounced for materials that are
very stiff at low temperatures than for polybutadiene propellants.
• £ g iassy/£oo ~ 1000 for polyurethanes, EDB, CDB and XLDB;
• £ g iassy/£ao ~ 500 for polybutadiene composite propellants.
The various behavioral criteria examined above provide a glimpse at the
behavior of propellants during the various loading zones (firing, storage, etc.).
However, to be able to judge the capability of a family of propellants to
handle a given load, we will have to analyze the result of a parameter
characterizing its behavior.
2. 2. 2. Mechanical resistance
2.2.2. 1 . Analysis of the most severe loads
(a) Long-term storage, thermal cycles, firing/ignition
In long-term storage and thermal cycles, strains inside the grain caused by
volumetric variations of the propellants are constant over time for a specific
range of temperatures.
This type of loading is similar to a relaxation test (constant strain), and the
behavior at relaxation is the parameter that must be studied.
Through experiments we have discovered that the maximum strain during
tensile test (e m ) is representative of that behavior.
In the firing of a case-bonded grain, strains are caused by the deformation
of the case resulting from pressurization occurring during ignition. This
phenomenon is comparable to a tensile test performed under temperature
and stress rates corresponding to firing conditions.
Main Families and Use of Solid Propellants 339
Assuming a linear elastic behavior, the resistance parameter will be the
pseudo-elastic deformation:
Four operating zones will be selected from the master curve of the propellants
investigated.
• Firing of a grain for tactical missile at low temperatures:
temperature, 9 = — 30°C (for example).
Ignition time: t { = 30 ms.
• Firing of a ballistic or space missile grain at ambient temperature:
temperature, 9 = 20°C,
Ignition time, = 200 ms.
• Thermal cycles of a grain for a tactical missile:
minimum temperature, 9 = — 30°C,
storage time, t = 200 h.
• Long term storage of a ballistic or space missile grain:
storage temperature, 9 = 20°C,
storage time, t = 10 years.
The pseudo-elastic deformation at firing and the strain at maximum stress are
indicated in Table 4, for all four zones described above.
Cold-temperature firing
The propellants best suited for firing at low temperature, using case-
bonded grains, are CTPB and HTPB, and XLDB.
Propellant types EDB and CDB, as well as the polyurethane composite of
Table 6, show insufficient deformation capability to withstand the case
deformation during firing.
Table 4 Propellant mechanical capability at firing and under thermal stress
Propellant
EDB
CDB
PU
CTPB
HTPB
XLDB
Low-temperature firing
e(%)
4.3
2.8
2.4
5.6
6
8.1
Ambient-temperature firing
e(%)
4.3
10.5
16.5
12.5
13
13.5
Cold cycle
ej%)
18.5
42
40
35
38
80
Long-term storage
e m (%)
24
60
20
35
42
60
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Alain Davenas
From a mechanical point of view they can be used only for free-standing
grains which are subjected to less stress at low temperatures.
Ambient-temperature firing
The HTPB, CTPB, polyurethane, CDB and XLDB propellants have a
greater capability than the EDB. Therefore, they will show a better mechani-
cal behavior at ambient temperature firing of case-bonded grains.
Cold thermal cycle
The CDB, polyurethane, CTPB and HTPB and XLDB propellants have
maximum strain above 35%, and consequently good mechanical resistance to
thermal cycles.
The elongation capability of EDB is definitely smaller ( e m ~ 18%), and
could, as a result, lead to some risks of rupture during severe thermal shock,
even for a free-standing grain structure.
Long-term storage (Fig. 7)
In this stress-strain situation typical of case-bonded grains HTPB, CTPB,
CDB and XLDB the best mechanical capability.
Even though CDB has a great deformation capability we cannot place it
ahead of the other propellants for this type of load, because the thermal
expansion coefficient plays a significant role, leading to an increase of the
thermal stress in the grains:
a p ~ 1 x 10 -4 °C“ 1 for composites
a p ~ 2 x 10 -4 °C“ 1 for CDB
10 3 -
Butalane HTPB
Butalane CTPB
Isolane
— Nitralane
EDB
CDB
1 o’ I 1 1 1 i i j
10 2 10 3 10 4 10 5 10 6 10 7 10 8
t/aT (mn)
Fig. 8.7. Long term storage behavior of various propellants.
Main Families and Use of Solid Propellants
341
2. 2. 2. 2. C on elusions
Analysis of the various parameters of the behavior and strain capabilities
of the main propellant families provides us with the following conclusions:
• Propellant grain for tactical missiles. From a strictly mechanical point of
view, only the polybutadiene and XLDB propellants can be used for case-
bonded grains, because of their good mechanical resistance during firing
at low temperatures. EDB and CDB propellants, as well as the polyureth-
ane propellant discussed above, can be used only for free-standing grain,
because of their high modulus and their low capability for deformation
under this particular stress. In this type of design, mechanical resistance
to thermal shocks is greater for CDB than for EDB propellants.
• Propellant grain for ballistic motors/missiles: = 20°C. The CTPB,
HTPB, polyurethane, CDB, XLDB propellants can be used in case-
bonded grains. However, CDB demonstrates the lowest mechanical
resistance to firing, as well as to long-term storage, due to its high thermal
expansion coefficient. The capability of the polyurethane tends to de-
crease under long-term storage: therefore the HTPB and CTPB and
XLDB propellants are preferable.
2.3. COMPARISON OF SIGNATURES AND SIGNATURE
CHARACTERISTICS
The most dramatic aspect is, of course, the visible signature which marks
the launching of a ballistic missile or the space shuttle with a huge plume of
white smoke. That visible smoke is characteristic of propellants with alu-
minum (primary alumina fumes). More generally, it is characteristic of
metallized propellants and in the case of ammonium perchlorate composites
without aluminum of the recondensation of hydrochloric acid when the
suitable ambient temperature and humidity conditions are present (second-
ary smoke).
Figure 8 shows the smoke occurrence, and illustrates its intensity for
various propellants under average climatic conditions in Europe.
In the case of a missile target that is followed visually, these smokes
completely mask the target and are absolutely unacceptable. As a result the
first generations of anti-tank or ground-air missiles were forced to use
homogeneous propellants. Today, these could be replaced by Nitramites
(minimum smoke XLDB propellants).
Today’s guidance systems rely mainly on the interaction of the plume with
laser beams within the infrared frequencies, requiring low absorption by the
combustion gases in the corresponding frequencies. Similarly, the infrared
signature resulting from the plume emission is often related to afterburning in
the atmosphere, which should be decreased or eliminated. The related criteria
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Alain Davenas
Secondary Smoke Secondary Smoke Propellants without
AP - AL Propellants, Propellants, AP, with
Propellants without AL AP < 1 5% Ballistic Modifiers
MZMMZZM i 1 1 i
Primary Smoke Aircraft Secondary Smoke No Signature
Condensation Trail from Missile
Condensation
Fig. 8.8. Appearance of visible signature of missiles in a European climate.
are more subtle. Some of the characteristics of plume emissions of propellant
gases are indicated in Chapter 5, and can provide initial direction.
2.4. COMPARISON OF MANUFACTURING PROCESSES AND
COSTS
Figure 2 gave an overview of the flow-chart for the production of
propellants.
EDB grains obtained by extrusion are clearly limited in their mass and size.
These limitations are mainly due to the size and the performance of the
presses that can be used. Diameters are generally limited to 250 mm in the
Western world.
Similarly, only cylindrical grains simple to manufacture, and therefore
inexpensive, can be produced.
The EDB process, on the other hand, lends itself particularly well to
industrial production as well as to high production rates. It is therefore
particularly suited for the production of small ammunitions, and for various
non-military applications. The homogeneity of this product and its high
degree of rigidity, allowing the production of very thin webs as well as the
possibility of machining within very precise limits (a few hundredths of a
millimeter), makes it very useful when seeking high-precision impulses. In
addition, the combination of rigidity and very thin webs is attractive for
grains combining short combustion times with high accelerations — useful
for light anti-tank missiles.
Main Families and Use of Solid Propellants
343
Finally, processes such as continuous screw extrusion and stamping may
well give new impetus to this product by contributing to a decrease in costs or
improvements in working conditions, production rates, or geometry (see
Chapter 9).
The CDB and CMDB propellants have the advantage of allowing the
production of free-standing grains in any type of shape with performances
that are comparable to that of the EDBs. Free-standing grains weighing
several tons manufactured by this process were used on propulsion stages of
US missiles. In France, free-standing grains weighing several hundred
kilograms are used in the sustainer motors of the Exocet missile family.
2.4. 7. The industrial cycles
The length of the production cycle is of critical importance for the client. It
is, of course, determined not only by the type of propellant but also by the
production capability available and by the number of specific tools and
equipment required for production.
All things being equal, a classification of the length of production cycles
would be in the following increasing order: EDB, composites or XLDB, CDB
(or CMDB).
The production of EDB grains with selected raw materials is almost
instantaneous as they are thermoplastics shaped directly. The length of the
cycle is controlled by finishing and quality control operations.
At the other end of the scale, the production of CDB is very slow, requiring
various intermediate production steps, as well as ballistic adjustment of the
casting powder, requiring firing test controls on specially cast specimens.
The decision to select a free-standing grain or a case-bonded grain is, of
course, greatly dependent on the industrial production of the motors. In the
case of free-standing grains the production of the cases and of the grains can
be done separately, allowing the creation of buffer stocks in case of produc-
tion difficulties in one of the other production lines.
2.4.2. Costs
The issue of the cost of propellants is important both for the client and the
manufacturer; it is also the object of many controversies.
Without pretending to do an in-depth analysis of this problem, it may be
useful to look at the subject and to determine several major factors. The cost
of a propellant grain is linked to four main parameters:
• cost of the raw material;
• manufacturing process;
• quantities required and delivery schedules stipulated;
• technical specifications, including conditions for acceptance and control.
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Alain Davenas
Of course, there is an interaction between the selection of the propellant
grain (and its manufacturing process) and the specifications requested by
the client. A constructive dialog is necessary to avoid certain specifications
unnecessarily increasing the complexity and thereby the cost of the pro-
pellant grain.
• When the volume and the duration of the manufacturing process allow
the organization of a specific production facility (as in the case of the
MLRS), the cost may decrease significantly.
• The cost of raw material may also be an essential factor, e.g. XLDB using
HMX of very specific particle size, or special nitrate esters (BTTN) are
intrinsically more expensive than a simple composite propellant.
Cost comparisons between various supplies in various countries are difficult
for at least two reasons:
• the quantities required and production schedules are rarely the same;
• the rules followed to determine cost (e.g. amortization rules, raw material
sometimes supplied free by the Government, investments that are or are
not compensated by the client) vary greatly.
Finally, the calculations are often expressed in terms of the cost of the
complete motor, and not of the propellant grain.
This raises the very interesting issue of the relative costs of various services
involved in the production of a rocket motor.
Gaunt has done an analysis of that issue [9] for ballistic missiles and
motors for space launchers. Figure 9 shows that the grain averages approxi-
mately 27% of the total cost. This ratio is very similar to observations made in
France. In these two specific cases, nozzles and the thermal protection are
especially expensive; that ratio is usually much smaller for tactical missile
Fig. 8.9. Breakdown relative costs for a large motor.
Main Families and Use of Solid Propellants 345
motors with a less sophisticated rear assembly, in which case the grain cost
can be as high as 50% of the total.
The same analysis demonstrates that the principal component of the
production cost for today’s rocket motors is labor (an average of 55% of the
total cost). Cost reduction is obtained through intensive automation, requir-
ing heavy investments that can only be amortized if very large programs are
launched.
Finally some simple things can be said for the cost of the different
propellant families:
• For composite propellants, the mass of propellant has a very important
effect on the price of propellant per kilogram.
• A precise comparison can only be obtained on a specific project. For
instance, for a small propellant grain (a few kilograms) for an anti-tank
system, we compared the cost of an EDB and CDB solution, both
compatible with the specifications, and discovered that their predicted
cost was so close that it was impossible to consider this parameter for the
final choice.
2.5. SAFETY AND VULNERABILITY CHARACTERISTICS
The client, whether the integrator or the end-user, is particularly interested
in these characteristics because they are the determining factor for size of final
assembly facilities, storage areas, conditions for transport, and hand-
ling and operations. The operational risks vary with the setting: for example,
the use of missiles under war conditions, or for space launchers, the risk of
lightning strikes on the launch pad, etc.
Here again, we must emphasize the relative and somewhat arbitrary nature
of individual national regulations that complicate attempts to establish
comparisons at an international level. Although the regulations tend to be
similar in their hazard classification of explosive substances, the classification
methods are not the same. An identical propellant or grain — CMDB, for
instance — can be found in a class 1.1 in the US (liable to detonate), and class
1.3 in France (see Chapter 7).
In addition, these classification tests were established for production,
storage and transportation purposes. Reactions to stimuli in operational
conditions are not necessarily well characterized by these tests.
For several years, in the wake of serious incidents, or accidents that
took on catastrophic proportions such as those on the American aircraft
carriers Forrestal and Nimitz , emphasis has been placed on the concept
of “lower sensitivity munition”. Missiles conforming to this designation will
be considered as “reduced risk ammunitions” (Munitions a Risques
Attenues — MURAT — in French) and “insensitive ammunition” in English.
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Alain Davenas
2 . 5 . 7 . Pyrotechnic threats from munitions
All munitions containing any energetic material (the term “munitions”
refers to armament devices of any caliber and includes mines, torpedoes,
missiles, and rockets) present pyrotechnic threats. Any munition that has
been subjected to unplanned stimuli (e.g. from a bullet or a shaped charge) is
not only likely to have been damaged, but its energetic material (gunpowder,
propellant, explosives) will probably also deteriorate or react. The reaction of
the munition generates thermal fluxes, a release of debris and shock overpres-
sures in its surroundings. The detonation of the first munition can induce a
reaction in other munitions nearby. The ensuing disaster may result in the
loss of the carrier, known as the combat platform (e.g. tank, helicopter,
aircraft, warship, aircraft carrier) with munitions aboard.
2 . 5 . 2 . Survivability of the combat platform
Today, these platforms are extremely expensive, and as a result are limited
in number. Defense organizations in various countries are greatly concerned
with the improvement of their survivability. Such an improvement involves:
• diminished detectability;
• diminished probability of being hit, once detected;
• reduced severity of the damage, once the platform has been hit.
The general improvement in the survivability of land, air, and sea platforms is
a major aspect of armament modernization. It requires a minimization of the
effects of explosive hazards from munitions subjected to unplanned stimuli,
contributing to the reduction of the vulnerability of the platform by limiting
the severity of the reaction and subsequent damage in a credible event.
2 . 5 . 5 . Basic corrective measures
These are as follows:
• protection with materials designed to reduce the impact of the stimuli,
barriers to slow down or prevent the propagation of the disaster, and
adapted storage configuration;
• intervention devices, including flooding, more or less automatic;
• modification of the cases containing the energetic material (for example,
pressure relief systems).
2 . 5 . 4 . Need for impro vements
The above measures have the advantage of being rapidly implementable.
Unfortunately, their application is not always practical. Protective materials
are often heavy, cumbersome, and they hinder the operation of the munition.
Main Families and Use of Solid Propellants
347
Worse yet, these remedies can, over time, turn out to be useless. The great
variety of scenarios of credible events makes it particularly difficult to
demonstrate the efficiency of these measures.
As a result, the expected minimization of severity could prove entirely
misleading. Recognizing this, various defense organizations and industry
leaders began to consider the possibility of lowering the sensitivity of
munitions, the third step in this process. Progress made in the area of
chemical explosives for nuclear warheads and explosives for mining and
demolition suggests the possibility of having munitions that reliably fulfill
their performance and operational requirements, but which are designed to
minimize their sensitivity.
2 . 5 . 5 . Lower sensitivity munitions or insensitive
munitions
The design of these new munitions, particularly at the research stage, must
be based on the following conditions:
• specially designed cases;
• revised inner configuration;
• energetic materials with limited reaction.
The last of these conditions, alone, could provide a satisfactory solution to
the problem, provided, however, that the survivability is not adversely
affected.
Specifications have already been introduced by the US Navy, the prime
force behind this activity. The related tests and criteria are shown in Table 5.
For propellants, the following data must be determined and provided:
• Test results for:
— slow cook-off,
— fast cook-off,
— sympathetic detonation,
— impact from multiple bullets,
— impact from multiple fragments;
• Critical diameter data.
The threat of fire, alone, is generally considered acceptable if thermal
explosions, and particularly detonations, are prevented.
Table 5 Tests and criteria for lower-sensitivity munitions
Slow cook-off
Fast cook-off
Bullet impact
Sympathetic detonation
Sensitivity to electromagnetic radiation
No reaction greater than fire
No reaction greater than fire
No reaction greater than fire
Unacceptable for storage
No explosive reaction
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Alain Davenas
Systematic research has been undertaken in various countries with the
purpose of establishing or completing the characterizations of existing
energetic materials. This research sometimes leads to unexpected results, and
the meaning or consequences of those results remain to be determined. An
example is significant variations in the critical diameter of polybutadiene-
AP-A1 propellants according to the percentage of ferrocene derivative in the
formulation [10]. All composites with ammonium perchlorate propellants
show very poor results in the slow cook-off tests.
It is too soon yet to have formed any conclusions on the respective merits
of existing propellants. A new perspective must be gained, and it will take
several years. Most likely, no existing propellant providing sufficient energy
will ever satisfy all requirements. For example: a sub-critical detonation
geometry requirement for double-base grains or XLDB could lead to a
considerable energy loss for smokeless propellants. However, various labs are
working on the development of lower-sensitivity high-energy smokeless
propellants, based on logical decisions such as those illustrated by Fig. 10.
Non acceptable
reaction
Physical
consideration
Deflagration to
detonation transition
1 — ► confinement
► transient
combustion
► sensitivity
to shock
High burning surface
(damaged material)
Risk reduction
Design a more resilient
less friable material
Higher ratio
of binder
Ratio polymer
plasticizer
Crosslinking
chemistry
Particle size of
the propellant grain
More energetic
compounds in
smaller quantities
To preserve a sufficient
New, more efficient
performance level, the
compounds must be
polymer must be energetic
synthetized
Fig. 8.10. Demonstration of how the formulation of an energetic material can reduce
the threats.
349
Main Families and Use of Solid Propellants
3. Additional Propulsion for Artillery
Increase in range and improvement of the accuracy of impact are two
major concerns in the design of artillery munitions. A technical solution to
satisfy these requirements consists of the injection, at low rate, of gases in the
vicinity of the base of the shell, to compensate partly or entirely for the
aerodynamic drag of the base.
The location of the ejectors will determine the selection of the configura-
tion:
• The systems with ejectors located at the very base of the projectile are
commonly known by the English term “base-bleed” [13]. This configura-
tion is illustrated in Fig. 11.
• The systems with ejectors located over the perimeter of the afterbody,
ejecting gases in the outer supersonic flow area, are termed external
combustion.
A description of the base-bleed system follows:
3.1. PRINCIPLE FOR THE DECREASE OF BASE DRAG
In modern artillery, base drag is 30-50% of the projectile total drag. It is
represented by the nondimensional coefficient, C x base, expressed by the
Fig. 8.11. Aft-end of a shell equiped with a base-bleed generator.
350
formula:
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C x base =
where p , p, and V stand for pressure, density and speed of supersonic outer
flow, base, base pressure.
By ejecting gases at a low rate directly into the low-pressure zone, the base
pressure can be raised, thereby decreasing the C x base drag coefficient.
The model of drag correction selected for combustion of a base-bleed grain
is taken from the works of the Swedish scientist, Hellgren [14].
C x corrected: C x total — C dec. C x base
with C x total: Total drag coefficient without base-bleed
C x base: Drag coefficient without base-bleed
C dec.: Decrease factor for the base-bleed effect.
The C dec. parameter is, essentially, a function of flight conditions, rate of
exhaust gases, and the shape of the afterbody.
The drag reduction effects increase with the V Q initial speed of the
projectile. The increased range of a maximum range firing is estimated at:
+ 20% for V Q = 800 m/s;
+ 25% for V Q = 900 m/s.
3.2. OPERATION SPECIFICATIONS FOR A BASE-BLEED GAS
GENERATOR
The base-bleed gas generator is designed to satisfy the following specifica-
tions:
• The internal configuration of the grain allows a highly regressive burning
surface versus web burnt, in order to obtain conditions of ejection during
the combustion while the missile is on its trajectory, so that the
characteristic or reduced flow rate is close to q — 5 x 10" 3 .
• The effect of mass injection at the base is defined by this adimensional
coefficient, called the characteristic flow rate:
P ao Vqo ^ b
m b = mass flow rate of the combustion gases injected to the base;
1% , Poo = speed and density of the surrounding air;
A h = surface of the base.
• To maintain the subsonic flow of the combustion gases, the pressure
generated inside the chamber must stay in the subatmospheric pressure
range. The composition used must offer satisfactory combustion stability
Main Families and Use of Solid Propellants
351
at this pressure range. Based on the firing conditions, the burning rate
level will be situated between the range of 1 and 1.5 mm/s at 0.1 MPa.
• The reducing combustion gases mix with the air of the outside flow and
cause a re-ignition phenomenon. This addition of weight and energy close
to the base reinforces the pressure increase effect.
The mechanical properties of the propellant are optimized so that the
generator can survive the stress induced in the cannon bore, where the
pressure and acceleration levels are very high.
The propellant selected allows operation within a wide range of
temperatures: —45 to +60°C.
• Asa rule, the materials and the implementation process are selected with
the idea of using industrial capabilities that are compatible with large
series production, with costs known to be acceptable in the artillery
sector, i.e. costs that are lower than those acceptable in the case of
missiles.
This type of production satisfies therefore two major criteria:
— limited cost and production time;
— manufacturing process easily adjustable to the various calibers used
in the artillery sector.
An acceptable solution that satisfies all of these specifications is a gas
generator made of a composite propellant (Butalites, i.e. reduced smoke
HTPB).
3.3. ROCKET-ASSISTED PROJECTILES
Another solution to increase the speed of the projectile on path is to apply
a thrust provided by the combustion of a rocket motor. These are known as
rocket-assisted projectiles: RAP.
The rocket motors necessary for an effect comparable to base-bleed are
very large and heavy, limiting the amount of explosive in the shell.
Finally, various countries are researching ramrocket or ramjet shells, with
the purpose of either increasing the range of classic artillery [15], or
propelling anti-tank arrow-piercing projectiles. This is expected to be fairly
long-term research.
4. Gas Generators and Their Various Applications
The first systems moved by gas generated by propellants or powders made
their appearance during the Second World War, in German combat aircraft
with ejection seats in 1944.
Propellant cartridges had also been successfully used to help in the starting
of piston-engine aircraft. A propellant cartridge with a high burn rate was
ignited in the engine combustion chamber, resulting in the starting of the
entire device.
352
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Since that time the use of gas generators has greatly expanded, and today
they have numerous applications in the aeronautics and space sectors, in
military missiles, and in some commercial activities [11,12].
These gas generators can be used in conjunction with many other existing
energy sources, such as:
• gas turbines;
• internal-combustion engines and electric motors;
• compressed gases and hydraulic accumulators;
• flywheels;
• batteries and fuel cells;
• solar cells.
These energy sources provide relatively varied application times, working
power levels, and density of stored energy.
The gas generators are classified in four major categories, based on the type
of propellants used:
• solid propellant gas generator;
• hybrid gas generator;
• liquid monopropellant gas generator;
• liquid propellant gas generator.
Further in the text, we cover only the solid propellant gas generators capable
of producing energy only once, for periods of times ranging from fractions of
seconds to several minutes at the most. These generators can nonetheless be
controlled, regulated, and in some cases even stopped and started several
times, although these latter types of generators are much more complex.
There are several types of solid propellant gas generators, based on their
application:
• Highly reducing gas generators used to produce gases to be burned in a
second step with the oxygen in the air. This class of generators include
essentially solid fuel generators used on ramjets.
• Hot gas generators designed to produce gases used to activate power
units such as hydraulic turbines, alternators, pumps, cylinders actuators,
etc. or to ensure auxiliary propulsion. In systems of this kind, the exhaust
gas temperatures of the generators are generally higher than 900-1000°C.
• Cold gas generators designed to supply gas to pressurize or inflate
systems incapable of handling high temperatures; in such cases the
temperature of the gas when it is used must always be lower than 300°C,
sometimes even below 100°C, requiring the use of cooling devices for the
initial gases.
The propellants used for these various generators have a formulation similar
to the classic solid propellants. Either homogeneous propellants or compo-
site propellants can be used, but the use of the latter is more prevalent these
days.
Main Families and Use of Solid Propellants
353
The technology and materials used determine the performance of each of
these various energy sources. Table 6 gives a list of energies that can be
produced by gas generators and by various competing systems.
We see here that gas generators are perfect choices for short operation
times of less than several minutes. According to the sort of energy required,
compressed gas and flywheel can also be used. Since the use of a gas generator
does not require the use of any valve, and it can be ignited by a pyrotechnic
device, the gas generator can be smaller, lighter, and offer quicker reaction
Table 6 Comparison of various energy sources in terms of applications and available energy
Energy source
Applications
Available
energy (in kW)
range
Gas generator
Auxiliary propulsion
Inflation
Liquid propellant tank pressurization
Thrust vector control
0.5 to 1000
Gas generator
with turbine
Hydraulic energy
Engine starter
Fuel pump
0.5 to 100,000
Gas generator
with turbine
generator
Auxiliary energy units for aircraft,
missiles or space shuttles
0.5 to 1000
Gas turbine
Transportation (ground, air, sea)
Auxiliary power units
Stationary energy
50 to 10,000
Internal combustion
engine
Transportation (ground, air, sea)
Stationary energy
Leisure vehicles
Portable tools
5 x 10' 3 to 1000
Pressure gas
Auxiliary propulsion
Inflation
Propellant pressurization
0.05 to 100
Flywheel
Toys
Public buses
Machines
5 x 10" 3 to 100,000
Batteries
Lighting
Toys
Engine starter
Emergency power
5 x 10“ 8 to 10
(per unit)
Fuel cell
Energy for astronautics
Stationary energy
0.05 to 10
(per unit)
Electric motor
Hand tools
Toys
Vehicles
5 x 10“ 4 to 100,000
Photovoltaic
solar cell
Energy for astronautics
5 x 10~ 3 to 20
354
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times than a compressed gas system. The problems caused by exhaust
pressure, temperature, and chemical composition can constitute, however, an
obstacle to their use.
When compared to a flywheel (rotating energy), the gas generator coupled
with a turbine has the advantage of always being ready to use.
The gas generator is a serious competitor to the gas turbine for utilization
times greater than 1 min, provided the total power required is less than
150 kW and the total operating time does not go beyond a few minutes.
When operation takes place without atmospheric oxygen, gas generators
are superior to all other systems, regardless of the operating time require-
ments.
The advantages over batteries can be demonstrated in the case where the
power required is relatively high (several hundreds of watts). It would include
the following uses, for example:
• composite propellants for power generators for ballistic or tactical
missiles;
• EDB propellant to propel submarine missiles out of their containers;
• EDB propellant, or CDB, for pressurization of liquid propellant tanks;
• composite propellants supplying very low CO contents for inflatable air-
bags used in case of collision in some automobiles (generally based on
NaN 3 propellants).
5. Pyrotechnic Compounds and Propellants for
Ignition Systems
The various pyrotechnic elements forming an ignition system for a
propulsion grain were introduced in Chapter 1: primary initiator, ignitor
initiator, and main ignition grain. For a detailed description of these
components, consult a pyrotechnics dictionary [16]. Table 7 provides a
description of the composition of an ignition system, and a typical igniter is
shown on Fig. 12.
The function of the main grain is to deliver a significant amount of hot
gases or a large number of hot particles in a very short time, a few tens of
milliseconds.
This rapid generation must satisfy two requirements necessary for the
ignition of the propulsion grain [17], as follows:
• creation in the volume surrounding the grain of thermodynamic condi-
tions (constitution of the gaseous phase, pressure, temperature), close to
the conditions of the grain’s steady combustion state;
• ignition by heat transfer of the igniter toward the propellant through
convection (transmission of heat flow), radiation (solid particles), or
conduction through solid or condensable particles;
Main Families and Use of Solid Propellants 355
Table 7 Constitution of an igniter : most commonly used components
Grain type
to ignite
Initiators
Increments or
main grain
initiators
Main grain
igniter
Large
Electric with high
energy level and ig-
nition threshold;
operated by shock-
wave or laser and
pyrotechnic com-
pounds.
Easily ignited pyro-
technic composition,
powder or pressed,
and usually generat-
ing a gas rate
adapted to the main
grain.
Free-standing case-
bonded grain with
high burning rate
composite or EDB
propellant.
Small
Usually
electric.
Same type, although
often integrated with
the initiator.
Either : same princi-
ple as for large
grains: ignition with
a micro rocket EDB
propellant or fast-
burning composite.*
Or. pyrotechnic
compound for igni-
tion generally com-
pacted.
* In such cases, the ability of the propellant to ignite is so high that it is possible to do without
the increment grain.
Fig. 8.12. Typical ignition system.
356 Alain Davenas
• component selection and design of the igniter can be done on the basis of
operating specifications (volume, ignition time, position in the motor,
safety, and cost).
Propellants
When the main ignition charge needs to be significant (ignition of large
grain), it will take the form of a small propellant grain. This grain must
present a large combustion surface which, coupled with a high burn rate, will
deliver a high flow rate. Composite or EDB propellant are particularly well
suited for this function.
Granulated or pelletized pyrotechnic compositions
These are used for initiator, increments and main charge in the case of
small grains, for which the volume to be pressurized is small. They are
discussed in Section 5.1 below.
For each of the pyrotechnic materials, the following information is
necessary:
• combustion temperature;
• flame temperature;
• nature of the combustion materials, and related gaseous volume;
• ignitability;
• safety characteristics.
5.1. FORMULATION, COMPOSITION AND CHARACTERISTICS
OF THE PYROTECHNIC MIXTURES
The powder or compact mixtures are composed of a fuel (metal) and an
oxidizer (oxide or fluoride) [18]. Once initiated, they are subject to a very
exothermic oxidation reduction reaction.
The combustion translates itself into the progression of a reaction zone
which separates the reacting elements from those which are not reacting yet.
The burning rate, i.e. the pressure rise time, is a function of the particle size
and of the reactivity of the oxidizer and the fuel.
Ignition mixture families and their main characteristics
Six major families exist today, with two or three elements each, and
differentiated by the fuel and oxidizers that are used. The first family (black
powder) is very old; the others were developed in conjunction with the
propellants.
The elements and major characteristics of these six families are as follows:
(a) Black powder
Black powder is a mixture of three ingredients: potassium nitrate (75%),
sulfur (12.5%) and charcoal (12.5%). It dates from antiquity and is still used
today as a powder or pellet ignition powder.
Main Families and Use of Solid Propellants 357
It is not very powerful (775 cal/g), highly gaseous, and easily ignited
(except in a vacuum).
(b) Aluminum and ammonium perchlorate mixtures
A powder mixture of aluminum flakes (40%) and ammonium perchlorate
(60%) powder. It is a very energetic composition (2500 cal/g), with a high rate
of gas generation, good ignitability, highly sensitive characteristics, and a
burning rate greatly affected by confinement.
(c) Aluminum , potassium perchlorate mixture
A mixture of two aluminums in flakes, with different reactivity (35%), with
potassium perchlorate (64%), and aluminum stearate (1%). This mixture can
be used in a powder form, although it is more often compressed into pellets, 1
to 6 mm thick. The aluminum stearate acts as a binder.
It is a very energetic composition (2500 cal/g), highly gaseous, possesses
very good safety characteristics, but is difficult to ignite, and its burning rate
is very dependent on pressure.
By modifying the ratio of the two types of aluminum it is possible to modify
the powder’s burning rate, and consequently the ignition characteristics (time
and pressurization).
(d) Zirconium-oxide mixtures
These are primarily binary mixtures of zirconium (37%), with copper oxide
(63%), or quadruple mixtures of zirconium (45%), with barium chromate
(34%), ammonium perchlorate (14%), and ammonium bichromate (7%).
These mixtures are used in the form of powders. They are moderately
energetic (700 to 1000 cal/g), but offer very good ignitability. They are,
however, very sensitive to electrostatic discharges.
The mixtures including CuO produce little gas but a large number of hot
particles. Mixture with barium salts and potassium yields a high volume of
generated gas.
(e) Boron and potassium nitrate mixtures [19]
These are essentially boron and potassium nitrate mixtures used in the
form of powder, or pellets or compact mixtures of nitrocellulose, boron and
potassium nitrate used in the form of micro-rockets.
These mixtures are moderately energetic (1500 cal/g), highly gaseous, have
very good ignitability and excellent safety characteristics. Their main draw-
back is their hygroscopicity.
358 Alain Davenas
(f) Magnesium-teflon-viton mixtures [20]
These powerful mixtures (2200 cal/g) can be compressed or extruded. Not
very gaseous, and with a moderate flame temperature, they offer very good
safety characteristics but are difficult to ignite.
The main performance and safety characteristics of these four typical
compositions are shown, respectively, in Tables 8 and 9.
5.2. MANUFACTURING PROCESSES
5.2 . 1. Powders
The homogeneity of the powder mixtures is obtained by using a mixer of
solids which consists of, for example, two containers and a rotation system
outside of the mixing zone. After drying has occurred, the oxidizers are placed
in one container, and the fuel in another. The whole is rotated for approxi-
mately 1 hour to ensure good homogeneity of the products. For safety
reasons all operations, including dividing into small quantities, weighing, and
closing of the containers, are done remotely with the use of a mechanical
remote control device.
5.2.2. Compacting
After homogenization the powder mixture can be compacted into pellets of
different sizes.
This operation is done with an automatic pellet machine with mold plate.
The various operations, including filling of the mold, molding, compression,
and ejection of the pellet, are done remotely and continuously.
The quality of the compacting is controlled through a crash resistance test
of the pellets.
Table 8 Performance of four powder mixtures
Mixture
Flame
temperature
(K)
Energy
(Cal/g)
Volume of gases
released
o/g)
Aluminum and ammonium
perchlorate
4500
2500
6.0
Aluminum and potassium
perchlorate, and aluminum
stearate (compacted)
4500
2500
4.0
Zirconium and copper oxide
2500
700
0.4
Zirconium and barium chro-
mate, and ammonium per-
chlorate and dichromate
3400
950
3.0
Main Families and Use of Solid Propellants
359
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360
6. Laboratory to Industrial Production:
Development Programs, Service Life, Research
Programs
6.1. GENERAL INFORMATION
The development of a modern weapon system, or of a space launcher, is
characterized by the simultaneous and interdependent development of com-
plex subsystems, whose production in conformance with the initially deter-
mined specifications and schedule spells the success or failure of the entire
program.
In addition, the technologies involved demand, as a rule, a very high degree
of development: high performance and reliability are usually the primary
characteristics.
Consequently, it is necessary to reduce to a minimum contingencies and
uncertainties at the beginning of the program, from a technical point of view
as well as from a financial one. This implies the use of proven technologies
and methods. Because the programs involved are long-term, complex, and
costly programs, and because many disciplines, professional specialities, and
industrial capabilities must be involved in a coordinated manner to reach the
goal, special program management methods and specific organizational rules
must be applied.
Under these conditions it is understood that, at the beginning of the
development of the propellant grain or of the motor, the products, processes
and methods to be used in the implementation of the program must be
sufficiently proven.
The terms research and development are used in the solid propellant
industry with a specific meaning.
The goal of the research is, generally, to develop and qualify materials,
processes, and measurement processes which will be used later in the
development of a motor or a propellant grain when the decision is made, by a
company or by government authorities, to develop a new system.
Propellant research, for example, must go from the laboratory phase,
involving several grams of the substances, to “Scale 1” at industrial facilities
capable of using several tons of the product. In the case of materials used in a
motor, research includes “exploratory development.” At this stage, however,
research is not immediately finalized. It will only be finalized through its
direct application in a system.
6. 1. 1. Definition of the term " development " and
general organization of development programs
According to the official definition, development is: “all activities with the
purpose of developing devices, processes or materials responding to well-
Main Families and Use of Solid Propellants 361
defined specifications, and which can be built or implemented in a reproduc-
ible manner”.
To use more precise terms, the purpose of engineering development is:
• to design and define the propellant grain responding to a specific need;
• to justify the design through tests, and if necessary, overtests, and by
simulated use;
• to establish mandatory production and control methods to ensure overall
quality of future industrial production;
• to prepare the industrial documentation for future industrial production
and quality control of the product;
• to determine, with the client, the conditions for acceptance of the future
series production.
6.1.2. Determination of the requirements , setting
of the specifications
The determination of the requirements must, however, be as detailed and
exhaustive as possible; it involves:
• a detailed look at the operational requirements of the future motor;
• expressing them in specifications for the grain.
The major types of specifications are described in Chapter 2.
Frequently, the determination of these specifications will require repetitive
steps. At this particular time, a joint review with the client of the impact of the
various specifications on the cost and final product quality for industrial
production, is of major importance. The techniques of functional or value
analyses applied at this stage provide a very efficient means of achieving the
optimization of cost and quality.
6.1.3. The program
The technical proposal forms the basis of the commitment of the company
or organization in charge of the development.
This technical proposal includes a development program, divided into
various phases. The logic of the activities planned within each phase, and the
sequencing of the successive phases, have to demonstrate that the objectives
of the program will be reached without major obstacles.
In France, as an example, the phases usually planned in a program are:
• development, tailoring, and manufacturing, testing to reach a final design
(“MAPI”);
• qualification by the contractor (“MAP 2”);
362 Alain Davenas
• official qualification of the grain (called certification when done by
governmental action);
• the industrial phase: implementation of the industrial facilities and
qualification of the production line.
The content of the program, in particular the number of tests performed, will
naturally vary as a function of the complexity of the grain and the degree of
innovation of the project. The length of the program will depend both on the
number of tests, and on the industrial cycle of the product considered.
Purely as an example, the number of tests necessary for a grain used in a
tactical application which requires to perform within a large range of
temperatures can vary from 10 to 20 (in a simple case), and 30 to 40 for the
development phase (MAP 1). The number of tests performed during the
internal qualification or certification phase is, of course, contingent on the
requirements of the client. The number of tests can also be determined by
requirements related to demonstration of reliability requiring overtests (more
stringent conditions) and to the performance of safety and vulnerability tests.
The duration of the development may vary from 2 years in exceptional cases
to approximately 4 or 5 years for tactical systems, and up to around 10 years
for strategic or space systems.
6. 1.4. Role of value analysis in the clarification of
the requirement during the preliminary
project and the project
This technique is designed to assist in finding the best compromise for the
definition of the product in terms of its performance and its cost. Briefly
described, a value analysis consists in giving responsibility to a group of
individuals, having various roles in the project, who together perform a
functional analysis of the product with the objective of finding a means of
reducing the production cost. It is a collective effort that should, to the extent
possible, include the client and the subcontractors, in order to arrive at a
functional expression of the requirement, the determining factor of the
product’s competitiveness.
6 . 1.5. Design to cost
This is the implementation of methods designed to control recurrent
industrial production costs for the product under development. This method
involves:
• identifying objectives for the recurring costs right at the beginning of the
development program;
Main Families and Use of Solid Propellants
363
• encouraging, through the inclusion of contractual incentives, the search
for and selection of technical solutions for both the cost objectives and
development requirements (quality, performance, schedule);
• managing the recurring costs during the development, the same as for
performance, quality and schedule.
6.2. PROGRAM MANAGEMENT
The methods described above, although included within the propellant
grain development, are not specific to propellants. They are, for the main
part, identical for the development of a motor, a missile, even an armament
system. However, with a growing number of sub-assemblies or basic opera-
tions, strict program management becomes increasingly complex, even for
propellant grains.
The program director needs to rely on increasingly complicated planning
and information tools.
The first activity consists in a breakdown of the program into basic tasks
and the creation of detailed flow-charts, known as the “work breakdown
structure” (WBS).
This allows decreasing the complexity of the project, identifying its main
components, and laying down a base for budgetary, scheduling and assign-
ments planning and control.
At the technical level, the use of relatively sophisticated planning tools (for
example, GANTT diagrams and critical path methods such as PERT), offers
the possibility of emphasizing the logic and the critical interfaces, and of
seeing whether the planning has been realistic. It results in a better apprecia-
tion of the principal difficulties, and the possibility of analyzing fail-back
solutions or alternatives.
At the program cost and budget control levels it provides the possibility of
having available, in real time, information necessary to evaluate the economic
performance by comparing expenses with work performed, and the remain-
ing expenses and work.
Nowadays, software systems for program management that integrate this
type of services are available commercially, and their use is becoming
increasingly frequent, particularly in the space industry.
6.3. SERVICE LIFE
This is one of the most difficult questions that will face the individuals in
charge of the development of a new motor or a new grain.
The client or prime contractor usually wishes to know the estimated
service life or— a direct consequence— the replacement cycle of the motors.
Unfortunately, that question can only be answered with great caution at
the beginning. As we will see later, it is therefore advisable to accumulate a
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maximum of relevant information, starting at the time of the research phase.
Similarly, it is necessary to use the greatest possible amount of information
that can be provided by results from the operational behavior of existing
motors and grains, whose designs are as similar as possible.
During the development, although at a time when the designs are
sufficiently determined (at the end of MAP 1, for example), it is possible to
start what is commonly known as “accelerated aging,” which will provide the
opportunity of estimating the potential life at the end of the development
phase. Ideally, to have the best estimate, the development phase would have
to last at least as long as the projected service life, and provided that the
impact of the various “treatments” the missile is subjected to when in use can
never be entirely simulated, have a limited impact. The principle of these
accelerated agings usually consists in using an increase in temperature to
increase the rate of the chemical phenomena responsible for the evolution of
the materials that make up the grain. Extreme caution is recommended,
however, because the failure processes can be of different natures, and the
temperature can impact differently on each of them, so that, in the worst case,
it is possible to create a failure that would not occur in the real application.
There have been such instances.
General recommendations in this regard are as follows:
• The temperature increases and accelerated aging must remain within
modest ranges to be representative.
• The samples, subjected to aging, must be as representative as possible of
the propellant that will be industrially manufactured.
• Not only non-destructive and firing tests must be performed on the aged
samples, but also detailed and analytic evaluations. It is these evaluations
alone that provide the capability of creating models of the evolution of
the safety ratio throughout the service life, as various properties of the
propellant change.
6.4. IMPORTANCE OF THE RESEARCH PHASE
We have determined that the teams responsible for the development of a
new grain must have access to proven technological tools, materials and
propellants, so that they may propose development programs that are short
and without contingencies.
The mission of the research teams is to supply these elements, and in
particular:
• create and validate methods to design the grains, estimate their service life
and estimate their operation under all types of working conditions;
• formulate, identify the characteristics, and implement up to the industrial
feasibility stage any new materials that are necessary for the progress of
the technology and the needs of the development.
Main Families and Use of Solid Propellants
365
Industrial considerations should be present very early during the research. As
much as possible they should be the principal factor in major decisions
concerning the various possible routes to reach the objectives selected for
density, specific impulse, burning rate, etc. This is particularly true for the
considerations of process costs and of raw material availability.
The last point is of particular importance for the continuity of the
industrial production, which in some cases can last for over 20 years, and for
systems which, when they are modified, require new certifications which are
extensive and expensive because of the interaction between the sub-assemb-
lies. The company supplying the propellant is rarely the manufacturer of all,
or even most, of the raw materials included in his products. The company is,
as a result, totally dependent on the industrial and commercial strategy of its
suppliers, or on official authorizations for imported products. It is therefore
advisable to ensure that the raw materials selected have solid long-term
guarantees, and to undertake, at the beginning of the research, actions such as
surveying substitute products, certifying second sources, preparing supply
agreements and so forth.
It is also necessary, when developing a new propellant, to test a sufficient
number of samples of those raw materials that have the greatest impact on
the quality of the propellant, to determine reproducibility and to have control
capabilities at a later time. Of course, these activities must be completed
during the development per se. Specific technical adjustment must be made
during the development phase, although the assessment of particular propel-
lants or materials for a new development must use this raw material
information base as much as possible.
Finally, it will be necessary to have, already at this stage, as much
information as possible concerning the aging of the propellant and related
materials under conditions similar to the future conditions of usage. This
requires that very early, during the research phase, programs be initiated to
learn about the mechanisms of degradation and the laws of evolution of the
products over time.
Based on the service life required for today’s propulsion systems, and the
limitations of accelerated aging methods in standard environmental condi-
tions, it is unfortunately rather rare to have a thorough knowledge of those
characteristics at the onset of the development of a grain. It is true that, for
older materials, their service life characteristics are well known, but these
materials do not have the performance characteristics now required. To gain
a better appreciation of grain life it is necessary to:
• strengthen the initial selection by using as much aging data as possible,
gathered from similar products under research, or from older grains with
practical experience that has been accumulated through monitoring
programs;
• perform, during the development phase, the evaluation programs de-
scribed previously.
366
Alain Davenas
This discussion emphasizes the importance of the role of the development
activity for the orientation of the research, and the inclusion of the research
within a broader perspective, which can be considered as being particular to
this type of industry.
6.5 ADVANCED DEVELOPMENTS AND EXPLORATORY
DEVELOPMENT MODELS
When very advanced technology is involved, an exploratory phase is often
included between the research phase and the development phase. Its purpose
is to confirm, at “Scale 1,” that the right combination has been made of
design method equivalents, processes, and materials in a new type of
propellant. This advanced development can be considered as the furthest
culmination of the research, and the surest way of having a shorter develop-
ment phase (because of the reduction of the number of tests required) without
any unpleasant surprises.
Bibliography
1. Klager, K., Polyurethanes, the most versatile binder for solid composite propellants. AIAA
84- 1 239— AIAA/SAE/ASME 20th Propulsion Conference, 1984.
2. Sutton, E. S., From polysulfides to CTPB binders— a major transition in solid propellant
binder chemistry. AIAA 84-1236— AIAA/SAE/ASME 20th Propulsion Conference, 19j$.
3. Martin, J. D., Polyvinylchloride plastisol propellants. AIAA 84-1237— AIAA/SAE/ASME
20th Propulsion Conference, 1984.
4. STEINBERGER, R. and Drechsel, P. O., Manufacture of cast double base propellant.
Propellants, manufacture, hazards and testing, pp. 1-28. American Chemical Society, Wash-
ington, 1969.
5. Lindner, V., Propellants. Encyclopedia of Chemical Technology (Kirk-Othmer), 9, 620, 3rd
edn., 1980.
6. Quinchon, J. and Tranchant, J., Poudres, propergols et explosifs— La nitrocellulose et
autres matieres de base des poudres et propergols. Technique et Documentation, Paris, 1984.
7. Calabro, M. et ai , Reverse forward dome for a missile first stage. AIAA 87-1989— AIAA/
ASME/ASEE 23rd Propulsion Conference, 1987.
8. Marguet, R., Ecary, C. and Cazin, P., Studies and tests of rocket ramjets for missile
propulsion. 4th International Symposium on Airbreathing Engines, Orlando, 1-6 April
1979.
9. Gaunt, D. C., Understanding costs of solid rocket motors. AIAA 86-1638— AIAA/ASME/
SAE/ASEE, 22nd Propulsion Conference, 1986.
10. Brunet, J., Detonation critical diameter of modern solid rocket propellants. ADPA, JISC,
New Orleans, 1988.
11. Cutler, H., Gas generators— perspective. AIAA 73-1168— AIAA/SAE 9th Propulsion
Conference, 1973.
12. Sutton, E. S. and Uriesen, C. W., Gas generators for aerospace applications. AIAA 79-
1 325— AIAA/SAE/ASME 15th Propulsion Conference, 1979.
13. Magnusson, A. I., Gunners, N. E., Ax, L. and Lundahl, K., Brevet suedois 76 104 8217.
14. Hellgren, R. V., Range calculation for base-bleed projectiles. 6th International Symposium
on Ballistics, 1981.
15. Mermagen, W. H. and Yalamanchili, R. J., Design and development of a ramjet tank
training round. 8th International Symposium on Ballistics, 23-25 October 1984.
16. Groupe De Pyrotechnie Spatiale, Dictionnaire de pyrotechnie, 3rd edn. CEDOCAR,
Paris, 1985.
Main Families and Use of Solid Propellants
367
17. Hermance, C. E., Solid propellant ignition theories and experiments. Progress in Astronau-
tics and Aeronautics , 90 , 239, 1984.
18. Calzia, J., Les substances explosives et leurs nuisances. Dunod, Paris, 1969.
19. Volk, E. et ai, Innenbalistische Bewertung der Wirkung von Anziindmitteln. 10th Interna-
tional Pyrotechnics Seminar, Karlsruhe, 2-5 July 1985.
20. Peretza, and Cohen, J., Development of a magnesium-teflon-viton composition for
propulsion system igniters. Israel Journal of Technology, 18 , 112-114, 1980.
CHAPTER 9
Double-base Propellants
HERVE AUSTRUY
1. Introduction
Propellants in which the binder consists of an energetic polymer plasticized
with a nitric ester, more particularly nitrocellulose plasticized with nitrogly-
cerine, are commonly called double-base propellants. The oxidizing and
reducing elements that are involved in the release of energy through
combustion are combined in the same molecule. In fact, nitrocellulose and
nitroglycerine bring together the carbon, hydrogen and oxygen necessary for
the chemical reaction. As a result these are known as homogeneous propel-
lants, in contrast to the composite propellants. And depending on whether
the manufacturing process is by extrusion or casting, they are also known in
France either as “SD” (solventless or extruded double-base propellants or
EDB), or as “Epictetes” (cast double-base propellants or CDB).
Double-base propellants are one of the oldest propellant families. Their
development is connected to the development of propulsion. At the end of
World War One, gun propellants were essentially colloidal powders with a
nitrocellulose base. The incorporation of nitroglycerine made it possible to
increase the energy level, and although the simultaneous increase of combus-
tion temperature limited their use as gun propellants, they became usable for
rocket motor propellants.
The applications for such rocket motors require tailoring of the combus-
tion pressure, burning time, over a wide operating temperature range, which
is activated by means of additives to the propellant. For the past 40 years,
propellant compositions have continued to evolve. The number of additives
has increased, and in some compositions where they represent 5-10% of the
total weight there are as many as 10 additives. These developments have
allowed a considerable increase in the quality, performance and reliability of
motors using double-base propellants.
Today, their development and use are linked to the economics of their
production and to some of their inherent charateristics such as:
369
370
Herve Austruy
• good mechanical properties including stiffness which is particularly well
suited for free-standing grains and for the manufacture of various
geometries with close dimensional tolerances;
• good aging capabilities, particularly under humid conditions;
• operational characteristics that are well suited to some specific applica-
tions such as:
— little or no solid particles in the gas jet, i.e. little or no primary smoke,
— little or no chemical elements likely to recombine with the atmo-
sphere to create secondary smoke,
— burning rates that are well under control and generally show little
sensitivity to the operational temperature.
2. Compositions and Raw Materials
2.1. FUNCTIONS OF THE CONSTITUENTS
The constituents of double-base propellants can be classified in five large
groups of products, based on their functions:
• energetic base constituents,
• additives for easier manufacture,
• chemical stability additives,
• burning rate additives,
• other additives for specific operations.
2. 1. 1 . The energetic base
The energetic base of double-base propellants is mainly composed by
nitrocellulose (40-70%) and nitroglycerine (15-41%). Other nitrated pro-
ducts are also sometimes used, such as nitroguanidine.
The manufacture of these propellants involves combining these two
products homogeneously, using a gelatinization process [1] which is based
on the mechanism of interaction between the nitroglycerine molecules
introduced in the network of the nitrocellulose macromolecules, and the
atoms or groups of atoms of these polymers. These mechanisms are
numerous, complex and governed, at a microscopic scale, by means of
attractive forces, ranging from Van der Waals forces (relatively weak
attractive forces), to hydrogen bonds whose energy may reach 12 kcal per
bond, and including dispersion forces, interaction forces between dipoles and
others.
The behavior of nitrocellulose in relation to solvents with a basic nature
has been the object of many studies [2]. These solvents include ketones, esters
and alcohols. The oxygen (basic) of carboxyl groups can interact with the
hydrogen (acid) of the secondary nitrated groups (CH-0-N0 2 ). This
Double-base Propellants
371
phenomenon is a function of a large number of parameters such as the degree
of nitration of the cellulose (referred to as percentage nitrogen in the NC), the
crystallinity, and the degreee of polymerization.
As far as nitroglycerine is concerned it is to be considered as a poor solvent
which does not form a true solution with the polymer. It does not penetrate
the organized zones of the polymer and swells only the amorphous interstitial
spaces according to a solvation process. One of the explanations is conside-
red to be the presence of oxygen links in the nitrocellulose molecule. Because
of the rigidity of the chains and their spatial organization, these oxygens have
a weak interaction with the nitrated groups of the nitrocellulose molecules.
The introduction of mobile solvents such as nitroglycerine permits bring-
ing nitrate groups closer to the vicinity of the oxygen links. This allows an
interaction to occur between the oxygens of the nitrocellulose and the acid
hydrogen of the CH-0-N0 2 group of the nitroglycerine. As a result a
portion of the nitroglycerine (30%) is used to solvate the nitrocellulose, the
remainder being more or less mobile within the network. At the macroscopic
level the beginning of the gelatinization process is often marked by a swelling
of the nitrocellulose fibers. The continuation of the process must be promoted
by a mechanical, thermal or chemical intervention, such as the addition of
another volatile solvent.
2. 1.2 . Additives for easier manufacture
These additives are necessary to facilitate the manufacture of the material.
These are essentially inert plasticizers designed to promote the gelatinization
phenomenon. They represent typically 0-10% of the propellant, and
phthalates or triacetate types are commonly used to desensitize the nitro-
glycerine for safer handling. Mechanical properties may also be modified.
Other additives, such as graphite, are used in very small amounts (below
0.1 %) to facilitate some operations; for example, the flowing of the casting
powders (Xenon powders) used for the production of CDB propellants.
2. 1 . 3. Stability additives
The nitric esters of double-base propellants decompose at rates dependent
on time and temperature. This decomposition corresponds to the rupture of
the 0-N0 2 bonds, and releases nitrogen oxides. Without a stabilizer, the
products resulting from the decomposition have a catalytic effect on the
decomposition reaction rate. The reaction is controlled when stabilizers are
included, which usually have a benzene nucleus capable of fixing the nitrogen
oxides by substitution.
An uncontrolled decomposition of the nitric esters could have serious
disadvantages:
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Herve Austruy
• From a safety point of view: since the decomposition is exothermic, there
could be a risk of ignition of the propellant when the energy released
becomes greater than the heat loss through exchange with the environ-
ment.
• From a quality point of view: there could be a risk of gas cracking of the
propellant when the decomposition kinetics of gas generation is faster
than the gas diffusion. This phenomenon is observed beyond a certain
thickness of the material. The critical size corresponds to the dimensions
where cracks appear at a given storage temperature.
• From a performance point of view: because the decomposition is
exothermic, the propellant energy — that is, the energy available for
use — would decrease with time.
The above emphasizes the importance of the selection of stabilizers in the
formulation of double-base propellants.
2. 1.4. Ballistic additives
The burning rate of double-base propellants varies greatly with pressure,
so that during their combustion in a rocket motor, small fluctuations in the
combustion are translated into significant pressure variations. As a conse-
quence, an accidental increase of the burning surface may result in an
overpressure that could lead to the explosion of the rocket motor.
Ballistic additives are added to the propellant to reduce the sensitivity of
the burning to pressure fluctuation, as well as to catalyze burning rates to the
higher regimes.
Some of these additives permit a burning rate independent of the pressure,
within a given range of pressures (the plateau effect). The plateau effect was
given its name because the burning-rate-versus-pressure curve has the shape
of a plateau. When the burning rate decreases with increased pressure the
phenomenon is called mesa effect. In the absence of such additives the
burning rate increases with pressure according to an exponential law.
Accordingly such additives are commonly referred to as ballistic modifiers or
burning rate catalysts, or sometimes as platonization agents.
The advantage of propellants with such plateau curves is obvious. Random
fluctuations of the burning area to throat area ratio result only in minimal
variations of the burning rates, and in very weak pressure variations. This in
turn enhances control, predictability and reliability of the motor perfor-
mance.
Furthermore these burning rate additives usually reduce the temperature
coefficient of variation of burning rate, enabling reduced motor performance
variability over a wide temperature range.
Double-base Propellants
373
P(MPa)
Fig. 9.1. Diagram burning rate-pressure of a double-base composition.
2 . 1.5 . Operational additives
Some characteristics peculiar to the use of a specific rocket motor or its
design may need some other additives.
Regardless of the configuration of the combustion chamber, the burning
rate must be stable, and this may require the presence in the combustion
gases of solid particles, such as refractory products to attenuate acoustic
combustion instability effects.
Special needs in terms of guidance or plume signature may require the
absence of re-ignition of the gaseous jet; flash suppressant additives may be
used to satisfy such requirements.
2.2. RAW MATERIALS CHARACTERISTICS
This section describes some of the characteristics of the principal ingre-
dients of double-base propellants with respect to their influence on process-
ing and final properties.
2.2. 1. Energetic raw materials
2.2.1. 1. Nitrocellulose
Cellulose nitrate, commonly called nitrocellulose, is obtained by action of
sulfonitric mixture (sulfuric and nitric acids) on cellulose. Such nitrate
esterification is in a heterogeneous phase reaction of mixed sulfuric and nitric
acids on cellulose fibers, in the course of which all three hydroxyl functions of
the cellulose may be nitrated to a greater or lesser degree.
The nitrogen content of the nitrocellulose represents the degree of nitration
of the available hydroxyls in the cellulose chains. Accordingly it indicates the
energetic level of the product.
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Herve Austruy
In France the nitrocelluloses are classified following a nomenclature
connected to the nitrogen content (in mass percentage). The more usually
used in a double-base production, are the following grades: CP X D, CP 2 L and
CP 2 U (13.1 N-12.6 N-11.7N).
(a) Solubility
The nitrocellulose solubility in polar solvents varies in accordance with the
nitrogen content.
The nitrocellulose grades insoluble in a given mixture of ether and alcohol
at 56° Baume are called type 1 (CP^. The soluble grades are called CP 2 .
(b) Viscosity
An important characteristic of the nitrocelluloses is the degree of polymeri-
zation or molecular weight, which is equal to the number of anhydroglucose
structural units forming the cellulose chain. This parameter principally
determines the viscosity of the nitrocellulose in a given solvent.
(c) Calorimetric value in calories per gram
The energetic properties of the nitrocelluloses are a function of their
percentage of nitrogen. Table 1 lists the major characteristics of nitrocellu-
lose, based on the French nomenclature.
2.2. 7.2. Nitroglycerine
Nitroglycerine or glycerol trinitrate resembles a colorless oil. It is obtained
through nitration of glycerine by a sulfonitric mixture. Its very high calori-
metric value (1750 cal/g) has led to its generalized use in double-base
propellants [4].
2.2. 1.3 . Other energetic ingredients
Beside nitrocellulose and nitroglycerine, other energetic products may be
used when special applications are involved. Nitroguanidine, for instance, is
used as a cooling agent or as a combustion moderator.
Other nitrate esters may be used either wholly or in part in substitution for
nitroglycerine. In particular the use of triethylene glycol dinitrate or butane-
triol trinitrate is noteworthy.
Double-base Propellants
375
TABLE 1 Major characteristics of different
nitrocellose qualities
Type
N%
Calometric
value (cal/g)
CP,D
^ 13.35
1060
CP,E
13 to 13.35
1040
cp 2 l
12.60 to 12.80
970
CP 2 P
12.40 to 12.59
940
CP 2 S
12.20 to 12.39
910
cp 2 t
11.80 to 12.19
870
CP 2 U
11.60 to 11.79
830
2.2.2. Process additives
2. 2. 2.1. Plasticizers
The most commonly used are:
• diethyl phthalate, a phthalic ester employed as a plasticizer for EDB
propellants;
• dioctyl phthalate, a plasticizer for CDB propellants;
• and particularly, in the CDB process glycerol triacetate or triacetin, as an
inert liquid mainly used in association with nitroglycerine in the casting
solvent. In this way the impact and friction sensitivity are reduced and the
gelatinizing behavior reinforced.
Other plasticizers sometimes used are:
• saccharose acetoisobutyrate, also acts as a burning rate modifier;
• ethyl phenyl urethanne, a plasticizer for EDB propellants;
• sucrose octoacetate;
• adipates such as ethyl, octyl, etc.
22.2.2. Other additives
Graphite is often used as a coating agent for the casting powder in the cast
double-base process. In low quantities (less than 0.1%) it reduces electro-
static charges and facilitates the powder flow into the casting molds.
Waxes (Candellila, Montant) in very small amounts, on the order of 0.5 %,
facilitate the extrusion process of solventless propellants. Some stearates,
magnesium stearate for example, have a similar role to the waxes.
376
2.2.3. Stabilizers
Herve Austruy
The molecular structure of stabilizers consists of aromatic benzene rings
suitable for reaction with nitro groups N0 2 arising from the decomposition
of the NC/NG nitric esters. The most common stabilizers are:
• Diethyl diphenyl urea or centralite acts as a stabilizer and also a
plasticizer for nitrocellulose. It is not suitable in charge grains of large
web thickness because the products of its stabilization reaction are gases
of poor solubility and diffusivity in the propellant. This can result in gas
cracking or fissures in the propellant.
• 2-Nitrodiphenylamine, which can act on the ballistic properties of the
propellant by increasing the burning rate and temperature coefficient. On
the other hand, diphenyl amine, a basic stabilizer for single-base powders,
cannot be used because of its reaction with nitroglycerine.
• N-methyl-para-nitro-aniline, with its very high capability of fixing the
nitrogen oxides, has an efficient stabilizing action, but also a more rapid
consumption and, consequently, quicker utilization of the stabilizer. Its
use is recommended for applications with high thermal stresses, or for
large size-grains. It is generally associated with one of the other stabi-
lizers, which ensures a longer lasting complementary effect.
• Resorcinol, which has a weaker stabilizing effect.
A certain number of other substances with aromatic cores compatible with
nitroglyerine can also be used, including, for example, 2-methoxynaphthalene
and trimethoxybenzene.
2.2.4. Ballistic additives
For double-base propellants the ballistic catalyst effect is obtained by using
metallic compositions [5,6], in particular lead salts or oxides.
The most widely used ballistic modifiers are lead salts such as dibasic
stearate, neutral stearate, salicylate, octoate, resorcylate, basic oxide (PbO),
and saline oxide (Pb 3 0 4 ).
These products affect the energetic level of the propellant, its burning rate,
the operational pressure range, and the manufacturing process. Consequently
their use and amount are dependent on the properties required, and vary
from one composition to another.
Copper-based products can be added to the propellant to strengthen the
effect of the other catalysts. Salicylate, octoate, oxides, and chromite are
among the most common copper compounds used.
Double-base Propellants 377
Finally, although alone it has a non-catalytic action, acetylene black is
widely used, because its efficiency becomes very high when associated with
other'catalysts such as lead or copper salts.
2.2.5 . Operational additives
The major particulate damping agents are zirconium oxide, zirconium
silicate, and silicium carbide. Various other products may also be used,
including tungsten and boron carbide.
After burning flash suppressants additives are potassium-based; they are
selected based upon:
• their efficiency in flash suppression;
• their chemical compatibility with the propellant;
• their influence on the propellant properties, in particular, the ballistic
properties.
Among the potassium salts used are, for example, cryolite, sulfate (the oldest),
bitartratre, and oxalate.
3. The Manufacturing Process
3.1. REMINDER OF THE FUNCTIONAL ROLE OF THE
PROCESS
The role of the manufacturing process is to ensure the transformation of
the raw materials into a finished product which is as close as possible to the
desired grain shape and size. Therefore, the manufacturing process provides
for a number of essential functions, such as the homogenization of the
product, its gelatinization, and its shape.
3.1.1. Homogenization
The various ingredients exist in very different physical states: floss for
nitrocellulose, liquid for nitroglycerine, and amorphous powder or crystalline
state for the ballistic catalysts. An intimate mixture must be ensured. There
are various techniques to be used, including kneading, screw extrusion, and
laminating between rollers.
All three of these techniques are used with solventless propellants. Solvent
kneading is used for the first phase of the production of CDB propellants.
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Herv6 Austruy
3 . 1.2. Gelatinization
Nitrocellulose gelatinization by nitroglycerine results in the swelling and
partial solution of the fibrous structure of the nitrocellulose.
A temperature increase facilitates the gelatinization. The rolling of EDB
propellants, for instance, is done at high temperature (100°C); the kneading
of casting powders at a temperature between 30 and 40°C; CDB propellants
are cured at a temperature close to 60°C.
Gelatinization is also facilitated by mechanical action during the mixing of
the casting powders and particularly, during the rolling of EDB propellant.
Finally, it is further facilitated by the use of the solvent system with an
acetone and alcohol base, or ether and alcohol, during the preparation of the
casting powders. These will modify the state of the nitrocellulose and the
absorption kinetics of the nitroglycerine by the nitrocellulose.
3.2. MANUFACTURING PROCESS OF EXTRUDED DOUBLE-
BASE PROPELLANTS (EDB)
3.2. 1. The conventional process
3.2 . 1. 1 . Manufacture of the paste: impregnation of the
nitrocellulose with nitroglycerine
Since the transport of nitroglycerine was forbidden, the mixing of nitrocel-
lulose and nitroglycerine has been done at the facility where the nitroglycer-
ine is manufactured. The process used, called “impregnation”, consists of
placing nitrocellulose in suspension in water agitated by compressed air, and
of pouring nitroglycerine, which disperses itself into droplets suspended in the
water medium under the effect of the agitation. These droplets are absorbed
by the nitrocellulose fibers with which they come in contact. The resulting
product, called a paste, is then homogenized and drained of excess water,
leaving a water content of 30% as required by law for transportation.
3.2. 1 .2. Drying of the paste
Too wet to be used in the manufacturing process, the paste is dewatered by
spin centrifuge for several minutes, reducing the water content to approxi-
mately 20 %.
3. 2. 1.3. Kneading
The water content of the paste is neither accurately known, nor is it
perfectly constant throughout the entire mass. A further mixing operation is
Double-base Propellants
379
necessary to obtain a homogenized product. The water content is also
measured, which allows calculation of the weight of dry nitrocellulose, and
therefore deduction of the amounts of constituents that need to be added
during the kneading operation. These other ingredients are added successi-
vely during the kneading, in small amounts for the solids and by spraying for
the liquids. At the end of approximately 30 min, the premixed paste obtained
is unloaded from the kneading machine. This paste constitutes a homoge-
neous unit, identified and used as such for the remainder of the manufactu-
ring process.
3.2. 1.4. Gelatinization: rolling operations
The removal of water from the paste and the gelatinization of the
nitrocellulose by the nitroglycerine is obtained by the dual effect of pressure
and heating, in two rolling phases.
During approximately 6 min, the agglomeration rolling is an essential step
for the gelatinization of the propellant and for the creation of the ballistic
properties. Because the rollers are rotating at various speeds, this operation is
also called differential lamination.
The sheets produced by differential rolling still contain too much water. A
further rolling, during approximately 15-20 min, perfects the gelatinization
and eliminates the residual amount of water. It is done with rollers rotating at
identical speeds, called a finish rolling.
3.2 . 1.5. Carpet rolling of milled sheets
Before they can be put into the barrel of the extrusion press the laminated
sheets must be rolled up to have a diameter slightly smaller than the diameter
of the barrel of the press involved. It is very important during this operation
to prevent heat losses.
3. 2. 1.6. Extrusion
Whether horizontal or vertical, an extrusion press for double-base propel-
lants always includes a barrel with a heating jacket, where very hot water is
circulated (70-80°C) and a piston moving inside the barrel. This is fitted with
annular air outlets. It is absolutely necessary to avoid blocking air into the
propellant rolls being compressed, because the air could become heated
through adiabatic compression, and cause ignition.
The press barrels have various sizes; they may measure up to 380 mm
diameter and hold up to 90 kg of propellant. The bottom of the barrel
consists of a sort of filter with holes, the “sieve plate” through which the
material is forced into a second barrel located just before the extrusion device.
The extrusion device consists of a die that determines the outside shape of the
free-standing grain or the propellant (cylinder, star, square, rectangle, etc.)
380
Herve Austruy
and of one or several needles to create perforations within the required shape.
When manufacturing large grains there is only one die per extrusion press;
but for small or mid-size diameters the extrusion press may be equipped with
up to 12 dies. The operations are performed in the following order:
• introduction of the roll into the press barrel;
• the piston is lowered to the surface of the propellant (approach of the
piston);
• vacuum process takes place to remove occluded air;
• the piston is set in motion, at a specific speed to effect the extrusion
process.
To guarantee a good stability of the dimensions of the sections extruded,
precise heat control is necessary to maintain the die at a uniform temperature.
Manufacturing quality depends on strict control of the extrusion operations.
Rheology studies have been done to determine the thermal and mechanical
mechanisms involved in the extrusion process [7]. A model reproducing the
thermomechanics of the flow inside the die has been developed that takes into
account the variations of viscosity as a function of the temperature and the
shear stress to which the propellant is subjected. The thermal phenomenon,
however, does not occur inside of the product, but at its surface. A boundary
layer is created, and its characteristics govern the flow and/or defects caused
by ripping. The conventional laws applied to molten polymers are not
capable of taking this boundary layer into consideration. Consequently, even
if its modeling is rather complex, the knowledge of the boundary layer
occurrence guides the choice of the geometry of the dies. For example,
profiles that have a propensity to break or disturb this boundary layer should
be avoided.
On exit from the extrusion press the strand or section of propellant swells,
because of the release of pressure. The higher the extrusion pressure, the
greater the swelling will be. To ensure the reproducibility of the swelling, the
extrusion pressure is set for the specific compositions, and the rate curve of
the descending piston is also controlled.
Typically the hydraulic pressures that are being exerted are approximately
18 MPa, resulting in a pressure on the material that may reach 70-100 MPa.
Safety rings limit the exerted pressure, and can be cut in case of fire.
3. 2. 1.7. Cutting
The extruded sections are roughly cut to be somewhat longer than the final
dimension.
3.2. 1.8. Machining
The propellant strands or sections, which undergo swelling to a larger or
smaller extent depending on the extrusion conditions, shrink during cooling.
Double-base Propellants 381
This phenomenon makes it difficult to obtain dimensions of close tolerances
without including a final machining.
Cutting to the final length is done after cooling has been completed,
sometimes even after an aging period. The cutting is usually done with a
milling saw. With the use of lathes, mills and drills, the outside and the inside
of the grain can be precisely shaped, according to requirements.
For the most part the cutting tool is cooled with fluid during the machining
operation, and the propellant machining swarf is removed from the vicinity
by vacuum exhaust.
3.2. 1.9. Inhibiting
Most of the grains for rocket propulsion must be inhibited on their outside
surface, as well as inside, in some cases. There are various techniques
available that depend on the size and the shape of the grains. They also
depend on the nature of the inhibition material. Typical materials are:
• filled or unfilled polyester cast inhibitors from prepolymers, with low
viscosity, and applied by a casting process;
• silicone polymer resins, applied by injection into molds surrounding the
propellant grain;
• polyurethane inhibitors, currently becoming increasingly popular, which
are injected around the propellant grain whose surface has been coated
with a primer.
3.2.2. O ther processes
The process described above is the process most widely employed for the
manufacture of solventless propellant grains. A significant amount of energy
is put into the material, giving propellants manufactured in this manner
excellent ballistic and mechanical properties. However,
• there are some variations in the manufacture of the propellant material
(calendering and stamping);
• new technologies, such as screw extrusion, already widely used for the
production of plastic materials, are replacing the conventional processes.
3.2.2. 1 . Calendering
Calendering permits the production of sheets or strips with a very regular
thickness, varying from 0.075 to 2 mm, and a textured surface, including ribs,
ridges, barbs, grids, and others variations.
382 Herve Austruy
The propellant sheets from the finishing extrusion rollers previously
described are passed through calender rolls. The latter is a powerful rolling
machine in which the rolls have a surface tailored to the propellant
manufacture. The rolls are also heated and have variable rotation speeds.
3. 2. 2. 2. Stamping (or hot forming)
Stamping is a hot forming process, or thermoforming, of propellant pieces
obtained by press or screw extrusion. These pieces are first cut to have
approximately the weight and size of the future grain [8]. The operation is
carried out in several phases:
• the propellant piece is placed in the mold, which consists of a die with the
desired outside profile and a stamp with the complementary geometric
profile required;
• the mold is closed, the temperature is raised to 80-90°C, the forming
temperature, and limited pressure is applied (3 kPa);
• the stamp is moved inside the die cavity to compress and force the
softened propellant to obtain the final shape desired;
• the stamp is removed from the die.
The advantage of this process resides mainly in the fact that it allows the
production of geometrical shapes that cannot be obtained by extrusion, such
as full head-end grains (where the central bore opens at only one end) and
elaborate and complex patterns which are difficult to obtain by extrusion.
3.2. 2.3. Screw extrusion
The production process for EDB propellants involves a large number of
successive phases, which are an economic handicap for the production of a
large number of parts.
Various attempts have been made to replace the EDB process with a more
continuous and economically more advantageous process (using solvents
and production in a non-solvent-liquid phase [9,10]).
The most complex attempts have sought to use the technology widely
employed for the production of plastic materials, i.e. the screw extrusion
process [11,12]. After a considerable period of adaptation this process is
currently used for the industrial mass production of EDB propellant grains
[13].
Two extruders are used successively; they are designed to perform the
following operations: agglomeration rolling, final rolling, and extrusion.
Kneading is the only separate operation that is retained, owing to the critical
importance of precise measurement of the quantities of the various ingredi-
ents in the propellant composition. These screw extruders include:
• a variable-rate feeding system;
Double-base Propellants 383
• a temperature control system for the screw and the die;
• a set of exhaust ducts to allow removal of water and gases;
• a die placed at the end of the extruder, used to shape the material.
The first extruder is fitted with an adjustable screw; this ensures the
gelatinization of the wet mixture. The mixture, transformed into granules, is
fed continuously to the second extruder. These granules can also be obtained
through a continuous rolling process. The second extruder, which is fitted
with two parallel screws, completes the homogenization of the mixture and
ensures the shaping of the material.
In addition to the economic advantages, this process is also a safer one,
inasmuch as the work can be done at a certain distance, does not require any
contact between the operator and the material, and reduces the amount of
handling and transfers.
3. 2. 3. Current products
There is a very wide selection of double-base extruded propellants. The size
range extends from very thin sticks (outside diameter 1.5-5 mm) to very large
diameter grains (around 500 mm).
Many extrusion profiles have been created, including end-burning grains,
multiperforated, and external star grains with cylindrical or star-shaped
central bores.
The weight of the grains varies from several grams, in the case of ignition
increments, for example, to a few tens of kilograms for ground-to-air missile
boosters.
The propellant manufacturing cycle is relatively short. The mixing, rolling
and extrusion operations can be done in just 1 day. This rapid production
feature of the solventless process makes it attractive for large-scale industrial
production.
3.3. MANUFACTURING PROCESS OF CAST DOUBLE-BASE
PROPELLANTS (CDB)
This process involves two main phases:
• Manufacture of the casting powder, which contains all of the nitrocellu-
lose and the solid ingredients, as well as a portion of the inert plasticizers
and, sometimes, nitroglycerine. This powder comes in the shape of small
cylinders with a diameter and length close to 1 mm.
• The casting and curing phase. The casting powder is placed in a mold. A
casting solvent — consisting mainly of desensitized nitroglycerine — fills
the interstices between the grains. Heating at moderate temperature leads
to a penetration of the casting solvent into the grains, resulting in the
creation of a homogeneous propellant grain [14].
384 Herve Austruy
3.3 . 1. Manufacture of the casting powder
3.3. 1. 1. Preparation of the raw materials
The raw materials are generally used without any special treatment. The
nitrocellulose, however, stored in a wet condition, undergoes a dehydration
by ethyl alcohol before it is used.
When the casting powder contains nitroglycerine, a premixing operation is
necessary. This consists of impregnating the dehydrated nitrocellulose with a
nitroglycerine solution in acetone. This operation is carried out in a mixer
equipped with one vertical blade slowly rotating.
3.3.1. 2. Kneading
All ingredients are mixed together with the suitable solvents in order to
obtain an extrudable dough. Although various solvents can be used for this
operation, the most common ones selected are mixtures of ether and alcohol
or acetone and alcohol.
The kneading, which takes place in a horizontal mixer with Z blades,
produces a uniform mixture of all of the powder ingredients and allows the
beginning of the gelatinization of the nitrocellulose in the presence of volatile
solvents and plasticizers. Various parameters govern this gelatinization:
• The amount of solvent is adjusted according to the compositions used
and, in particular, to the quality of nitrocellulose. The solvent to dough
ratio or percentage has a significant influence on the solvation/gelation of
the nitrocellulose and, as a result, on the ballistic and mechanical
properties of the final propellant.
• The composition of the gelating solvent, i.e. the relative proportions of
ether and alcohol, or acetone and alcohol.
• The introduction order of the ingredients. The nitrocellulose, if necessary
premixed with the nitroglycerine, is introduced first, and the mixing
operation is begun with the solvent so as to prepare a dough which will be
ready for the subsequent homogenization of the various ingredients:
plasticizers and ballistic catalysts.
• The temperature, generally maintained below the boiling point of the
solvent, at approximately 30-40°C.
• The duration of the mixing operation, usually less than 4 h.
3.3. 1.3. Extrusion
After the mixing, the dough is compacted into the barrel of an extrusion
press which, unlike the presses for the solventless propellants, does not
require a fine heat control or vacuum system. The operation is controlled to
Double-base Propellants
385
ensure a constant extrusion speed, because this speed has a direct effect on the
size of the extruded sticks (diameter close to 1 mm). The behavior of the
dough at extrusion is largely a function of its composition and of its
gelatinization state [15].
3.3. 1.4. Removal of solvents
The cords produced by the extrusion press are placed in an oven in order
to remove most of the residual solvents. As a result the sticks get a certain
hardness, which makes them easier to cut.
3.3. 1.5. Cutting
The quality of the cutting, typically using a guillotine technique, is
important, because it directly influences the bulk or packing density of the
powder. Typically, the length of cut is equivalent to the diameter of the sticks,
i.e. 1 mm.
3.3.1. 6. Final drying
Most of the solvents have been removed in the course of the previous
operations; however, residual solvents are caught in the nitrocellulose fibers,
and a simple heat conditioning may not be sufficient to remove them
completely. Consequently, the next step may involve soaking the product for
several days in hot water (60-80°C). This hot water medium facilitates
removal of the solvents. Water has little chemical affinity with nitrocellulose,
and can easily be removed by hot air drying (60°C). The proportion of
volatile material in the powder is reduced to a value close to 1 %.
3. 3. 1.7. Finishing
After the drying phase, the casting powder is often coated with graphite.
This reduces the powder electrostatic charges and facilitates its flow proper-
ties. This operation also permits a deburring of the grains, i.e. a removal of the
surface roughness, increasing the bulk or packing density of the powder. This
operation is carried out either in a batch process in a mixing tower or a
coating machine, or in a continuous process in a hopper with an endless
screw.
The powder sub-batches obtained are mixed together to form a large
homogeneous blended lot of casting powder. This operation is an essential
one, because the uniformity of the properties of the cast propellant are largely
determined by the properties of the casting powder.
386 Herve Austruy
3.3. 1.8. Control of properties
A certain number of the characteristics of the casting powder are systemati-
cally controlled:
• the water and volatile material contents in the finished powder are limited
respectively to 0.7% for water and 1.8% for the volatile materials;
• the apparent density or gravimetric density, which determines the pack-
ing or volume loading of the grains in a column of powder, and is
consequently directly related to the final composition of the propellant;
• the chemical composition and, in particular, the amount of stabilizers,
ballistic catalysts and graphite;
• the thermal stability, which is monitored by a sample heat test, where the
temperature is raised up to 108. 5°C or 120°C — the time required for the
emission of nitrogen oxides is determined;
• the heat of explosion, which determines the final energetic properties of
the propellant.
3.3.2. Manufacture of the casting solvent
The casting solvent is a mixture of nitrate esters and inert plasticizers. The
latter are called desensitizers because they decrease the sensitivity to shock
and friction of the nitrate esters.
The most commonly used solvents are obtained by mixing nitroglycerine
and triacetin, which is a good desensitizer of nitroglycerine (Fig. 2).
Values for the following parameters are chosen to meet the requirements of
particular applications and the desired performance:
• percentage of desensitizer (between 21 % and 27 % in most cases),
• percentage and the nature of the stabilizer (between 0.5% and 1 %).
Fig. 9.2. Sensitivity to 30 kg fall-hammer test of casting solvent as a function of the
quantity of triacetin.
Double-base Propellants
387
The casting solvent is produced by introducing the nitroglycerine into a
premix containing triacetin and the stabilizer. A dehydration process is
carried out by heat treatment — under vacuum accompanied by pappling or
bubbling dry air through the mix. A water content of less than 500 ppm is
attained.
3.3.3. Manufacture of the cast double-base
propellants
The objective is to obtain a homogeneous product by gelatinizing the
casting powder with the casting solvent.
3.3.3. 1. Fitting of the molds
The casting powder is loaded into a casting mold that consists of the
following parts:
• a base to allow the positioning of the casting corset and ensure a good
distribution of the casting solvent;
• a metal casting corset or tube which will give the propellant blank grain
its outside shape;
• a metal core to shape the central bore of radial burning grains;
• a top assembly to seal the mold, which includes a vacuum system and a
sighting system allowing a check on the casting solvent injection.
The powder packing density generally reached is around 65%. This is a
function of:
• the size of the casting powder grains — theoretical calculations reveal
that the grain arrangement is optimum when the length versus diameer
ratio is close to 1.
• the method by which the casting powder is introduced — various me-
thods have been used to best fill the molds: vibrations, successive sieves
with cross mesh and bars set in a spiral along the filling funnel;
• the characteristics of the casting powder itself: apparent density and also
the surface condition, which in turn depends on manufacturing condi-
tions, quality of the nitrocellulose, and powder nitroglycerine content.
Once the mold has been filled with powder a degassing phase, carried out
under reduced pressure at ambient or moderate temperature and lasting a
few hours, removes the residual volatile solvents and the air contained in the
mold.
Herve Austruy
388
3.3.3. 2. Casting
The casting consists of injecting the casting solvent into the base portion of
the mold serving as a distribution chamber, and subsequent passage through
the powder bed.
The interstices between the casting powders are filled with the casting
solvent or gelatinizing liquid. Modeling studies of this phase [16,17] have
revealed significant behavior variations, depending on the state of gelatiniza-
tion and the nature of the casting powders.
3.3.3.3. Curing
Following casting the mold contents are subject to a curing process. This
accelerates the gelatinization of the nitrocellulose by the casting solvent. The
diffusion of the solvent is assisted by the presence of the triacetin molecules,
which have a significant affinity for nitrocellulose. This phenomenon cor-
responds to more or less active interactions between the plasticizer and the
nitrocellulose polymer, and causes a slight exothermic effect [18].
The curing process varies within different countries; it includes either one
curing phase or two distinct steps:
• A precuring of 24-72 h, at a temperature of approximately 40-45°C,
letting the grains absorb the maximum quantity of solvent necessary to
make them swell. During this precuring phase the casting powders are
already sufficiently gelated and coalesced to each other to allow the
removal of excess casting solvent. This is necessary to avoid a risk of
decomposition of the nitroglycerine in the surplus liquid during the
second curing operation.
• The curing itself, which completes the migration of the solvent to the core
of the nitrocellulose fibers.
As the curing progresses, the core of the granules becomes increasingly
translucent and, after a few days, the entire grain is transformed into a
homogeneous substance. The propellant has then attained its finished
mechanical and ballistic properties. The entire operation requires periods of
more than 72 h and temperatures ranging from 50 to 65°C (Fig. 3).
During the curing phase the propellant undergoes variations of volume
whose magnitude depends on the degassing conditions of the powder and the
solvent. These variations correspond mainly to the filling of the microporosi-
ties of the granules of the casting powder (Fig. 4).
3. 3.3 .4. Mold disassembly
Disassembly consists of removing the core from the propellant grain and
drawing the grain from the casting tube.
Double-base Propellants
389
Fig. 9.3. Diagram of mechanical properties set up of a cast double-base propellant as
a function of the curing conditions (time-temperature).
Conditioning of
the casting powder
Conditioning of
the casting solvent
Casting
Curing
t =
40°C
1
0 =
P atm
40‘C
P =
t = 4H
2 H
40°C
2
0 = 40°C
40°C
P atm
40°C
P = 5 mm Hg
5 mm Hg
10
20 30 40 5i
Curing time (hours)
Fig. 9.4. Diagram of the volume variations of a cast double-base propellant as a
function of the conditioning of the casting powder and of the casting solvent.
3.3.3. 5. Machining
The ends of the propellant grain must be removed because their composi-
tion is slightly different due to the fact they were in proximity to the excess
solvent during the precuring operation.
The grain is then cut to the proper dimensions using the same techniques
as for extruded propellant grains (Section 3.2.).
390 Herve Austruy
3 . 3 . 3 . 6 . Inhibiting
The process used to inhibit double-base cast propellants is the same as the
process described for extruded propellants (Section 3.2.).
In some instances there are advantages for other techniques when applica-
tion allows it (small or medium-size grains with fairly regular external
profile). These techniques involve casting the propellant into the inhibitor by
using a insulator as a casting mold. This operation offers the two following
advantages:
• the machining operation is no longer necessary because the grains are
cast directly in the dimensions required (except for the length of the
grain);
• the final inhibiting operation is not necessary.
3.3.4. O ther processes
The evolution of double-base cast composition toward increasingly ener-
getic propellants has imposed some modifications to the process. For
instance, the search for high contents of nitrate esters (nitroglycerine, for
example) led to partly incorporating them into the casting powder, requiring,
as a result, two modifications:
• the addition, already mentioned, of nitroglycerine to the nitrocellulose in
a premixing phase;
• the exclusion of the water steeping phase, since the presence of high
amounts of plasticizers facilitates the elimination of the volatile solvents.
The screw extrusion technique can simplify the process of obtaining casting
powder. The performance characteristics of propellants made from such a
casting powder are similar to that of propellants obtained by the conven-
tional process.
3. 3. 5. Current products
The casting technique permits the production of propellant grains with
virtually no limitations as far as shape is concerned, except for the height of
product cast, although these can be as high as 2 m.
Many varied types of propellant grains are produced, such as end-burning
grains, grains with cylindrical or star-shaped center bore, with variable
profile such as partially slotted tubes, or dual propellant grains.
Their size may vary from a few grams to several hundreds of kilograms.
Because the cast double-base propellant technique has been thoroughly
mastered, it allows the production of large industrial quantitites; for example,
sustainer propellant grains for anti-tank missiles.
Double-base Propellants
391
4. Characteristics of Double-base Propellants
4.1. PHYSICOCHEMICAL CHARACTERISTICS
4 . 1. 1. Density
The density of double-base propellants results from the density of their raw
materials: nitroglycerine (1.60), nitrocellulose (1.650-1.662). However, it is
also influenced by the density of the additives: lower-density non-energetic
plasticizers and higher-density ballistic modifiers. Typically:
• 1.55 to 1.66 for EDB propellants;
• 1.50 to 1.58 for CDB propellants.
4. 1.2. Linear thermal expansion coefficient
The coefficient determines the geometrical changes to the grains as a
function of temperature, and consequently, permits assessment of the toler-
ances required inside the combustion chambers. This coefficient is character-
istic of the nitrocellulose, nitroglycerine and plasticizer mixture, and is
approximately 1.2 x 10 _4 .
4. 1.3. Specific heat capacity
Characteristic of the nitrocellulose-nitroglycerine matrix, the specific heat
capacity is approximately 0.350 calorie per gram per degree for all double-
base propellants.
4.1.4. Thermal capacity
Derived from the previous characteristics (specific heat, density) this is in
the range of 0.570 calorie per gram per cubic centimeter.
4. 1.5. Thermal conductivity
This property governs the heat exchanges inside a grain subjected to
varying thermal environmental conditions. The reference value of 10 x 10 4
watt per centimeter per degree means that these propellants are a relatively
insulating material.
4.1.6. Heat of explosion
The heat of explosion of the propellant is directly tied to its energetic level.
Based on the respective ratios of the various ingredients, the two double-base
propellants cover the following ranges:
392
Herve Austruy
• from 700 to 1100 cal/g for EDB propellants;
• from 500 to 900 cal/g for CDB propellants. The low values correspond to
compositions with high contents of inert plasticizers, used as gas genera-
tors.
The heat of explosion of a propellant is equal to an additive value characteris-
tic of each of its constituents. Table 2 gives the theoretical values for the
major constituants of double-base propellants.
Table 2 Heat of explosion of the main ingredients of double-base
propellants
Potential (cal/g)
Slabs
Nitrocellulose
+ 800 to 1080
Nitroglycerine
+ 1750
Nitrocellulose/nitroglycerine paste: 74/26
+ 1070
66/34
+ 1180
62/38
+ 1250
60/40
+ 1190
59/41
+ 1270
58/42
+ 1280
50/50
+ 1350
Additives
Centralite
-2440
2 Nitrodiphenyl amine (2NDPA)
-1548
Diethylphthalate
-1765
Dibutylphthalate
-2070
Triacetin
-1253
Neutral lead stearate
-2103
Basic lead stearate
-1264
Lead salicylate
- 915
Lead octoate
-1331
Pb 3 0 4 minium
+ 139
Lead oxide (PbO)
+ 68
Copper octoate
-1941
Copper chromite
+ 245
Potassium cryolite
- 14
Potassium sulfate
+ 222
Potassium nitrate
+ 1428
Acetylene black
-3395
Magnesium stearate
-2806
Aluminum
+ 3656
Candelilla wax
-3277
Magnesium
+ 3214
Copper oxide (CuO)
+ 367
Dinitrotoluene 2-4
- 150
Dinitrotoluene 2-6
- 72
Ethylphenylurea
-2236
Double-base Propellants
393
4.2. MECHANICAL CHARACTERISTICS
Over the course of their service life, solid rocket motors are subjected to
various stress factors (such as acceleration, vibration, shock, thermal effect,
and others) which need to be compared with the mechanical capability of the
propellant. A certain number of characteristics determines the propellant
mechanical capability, including those discussed in the following paragraphs.
4.2.1. Hardness
Hardness is a quick and simple way of assessing the mechanical properties
of a material. The values usually obtained at 20°C are about 55 shore A.
4.2.2. Tensile and compression behavior
Double-base propellants are characterized by high elastic moduli and
mechanical properties suited to use in free-standing grains, sometimes with a
very thin web.
These characteristics are most commonly determined by performing
uniaxial tensile tests. The JANNAF specimen, dumbbell type, is most widely
used. A complete mechanical characterization of the properties of a propel-
lant needs the performance of a large number of tensile tests in order to test
the behavior of the material within a wide range of times and temperatures. A
sample of the master curve ( Sm , E , e, em) of an EDB propellant is given in Fig.
5. Table 3 is a mechanical characteristics example of an extruded and cast
composition.
Table 3 Comparison of the mechanical properties of an EDB propellant and a CDB
propellant
— 40°C
+ 20°C
+ 60°C
EDB Propellant
Sm (MPa)
51
11
2
e(%)
2.8
2.5
8.0
E (Mpa)
1835
439
21
«,(%)
3.4
15.7
31.8
CDB Propellant
Sm (MPa)
33
11
3
e(%)
1.0
2.0
10.7
E (MPa)
3279
555
27
«,(%)
1.2
24.5
66.8
394
Herve Austruy
Curves Sm andE
t/a T (mn)
Curves e and em
t/a T (mn)
Fig. 9.5. Master curves for an E.D.B. propellant.
4.3. KINETIC CHARACTERISTICS
4.3.1. Burning rate
The burning rate of homogeneous propellants depends primarily on the
ballistic modifiers in the composition.
Figure 6 and 7 show the performance currently available. The range of
burning rates of EDB propellants, at 20°C, is between 5 and 40 mm/s, while
the range of CDB propellant is narrower, from 3 to 20 mm/s.
50
40
| 30
E
r 20
10
o
P(MPa)
Fig. 9.6. Range of burning rate-pressure available to E.D.B. propellant.
0 5 10 15 20 25 30 35 40 45
Double-base Propellants
395
Fig. 9.7. Range of burning rate-pressure available to C.D.B. propellant.
The plateau effect is found in a pressure range which depends on the
burning rate. Consequently, at 5 mm/s the plateau pressure is around 5 MPa,
while at 40 mm/s it is approximately 30 MPa.
4.3.2. Temperature coefficient
The temperature coefficient expresses the sensitivity of the propellant
burning rate to its temperature before combustion. Where homogeneous
propellants are concerned the values obtained vary greatly, depending on the
composition :
— 7r k = 0. The burning rate is independent of the temperature. This pheno-
menon is observed, in particular, for EDB propellants with low energetic
levels (lower than 900 cal/g).
— n k < 0. As the temperature before combustion goes up, the burning rate
decreases. This type of value if found mainly wih CDB propellants with low
energetic levels (of the order of 700 cal/g).
— 7i k > 0. This is the most frequent case with these propellant families. The
values obtained are in the range of 0-0.3% per degree; a few higher values
can be found with highly energetic propellants (higher than 1100 cal/g).
4.3.3. Parameters affecting the burning rate
The burning rate depends mainly on the nature of the catalytic system.
Besides this major factor, there are other parameters worthy of notice.
4.3.3. 1 . A djustment
Certain elements such as acetylene black, by varying very slightly the
amounts used, can significantly change the burning rate. This property is
396
Herve Austruy
used to guarantee a perfect reproducibility of a specific composition, regard-
less of the various raw materials lots.
4.3. 3.2. Ballistic modifiers particle size
Some of the catalysts can influence the burning rate with their particle size.
This effect is of relatively modest importance; it has been seen with certain
oxides (CuO, for instance). The particle size of the catalysts typically is of the
order of a few microns.
4.3.3. Manufacturing process
The processing may also have an impact on the ballistic properties of
double-base propellants, inasmuch as they influence the homogeneity of the
catalysts’ distribution and the gelatinization of the product. This effect was
demonstrated with both propellant families.
(a) Extruded double-base propellants
The duration of the agglomeration rolling operation (done in the presence
of humidity) can be significant in some cases to the level of the final ballistic
performance. There is a decrease in the pressure exponent and the creation of
a plateau effect by prolonging the duration of this rolling operation [19].
(b) Cast double-base propellants
The gelatinization phenomenon is, for this family, mostly due to the
chemical action of the solvent used to manufacture the casting powder. As
such, the amount of solvent introduced in the mixer and, in particular, the
quantity of acetone, are likely to have an influence on the characteristics of
the final propellant. A large quantity of acetone promotes the gelatinization
and makes the fibrous structure of the nitrocellulose disappear. Casting
powder, in an advanced state of gelatinization, has less affinity for the casting
solvent, which will have more difficulty in penetrating inside the casting
powders. The final propellant, as a result, will be more heterogeneous and the
ballistic properties, which are related to the homogeneity and the state of
gelatinization, will therefore be modified.
(c) Comparison of EDB and CDB processing techniques
Both processing techniques have been tested for the manufacture of
double-base propellants. The EDB process leads to a better-gelatinized and
more homogeneous product, because of the efficiency of the mechanical and
Double-base Propellants
397
25
20
15
10
51 -
q
Extruded Double-Base Propellant
Cast Double-Base Propellant
10
15 20
P(MPa)
25
Fig. 9.8. Influence of the manufacturing process on the ballistic characteristics of a
double-base propellant.
thermal actions of rolling. A comparison of the ballistic properties (Fig. 8)
reveals a higher burning rate for the EDB propellants.
4.3. 3. 4. Energetic level
The plateau effect of the double-base compositions is obtained by using
catalytic systems tailored to the energetic level of the composition.
The plateau burning rate is related to the super-rate effect caused by the
ballistic modifiers. The result is that a high energetic level leads naturally to a
high burning rate.
The energetic level also has a significant impact on the temperature
coefficient, which generally increases with the energy of the compositions.
4.4. ENERGETIC CHARACTERISTICS
The energetic characteristics are usually expressed in terms of specific
impulse (in seconds). As an alternative to the necessity of systematic
experimental measurements on standard grain, various simplified ap-
proaches have been used to determine the energy characteristics of a
propellant:
• the theoretical specific impulse, derived from thermodynamic calcula-
tions;
• the heat of explosion, corresponding to the measurement of the calorie
value during the combustion of the propellant.
4.4. 1. Theoretical performance
The theoretical performance of a given composition may be calculated by
taking various parameters into account, such as:
398
Herve Austruy
• atomic composition of the propellant (C, H, O, N and others);
• chemical equilibrium in the combustion chamber;
• combustion conditions (gas expansion).
4.4.2. Heat of explosion
The heat of explosion, expressed in calories per gram, permits a simple
measurement of the energetic level. The operation is carried out in a
calorimetric closed vessel, and consists of measuring the rise in temperature
of a specific quantity of water during the combustion of a specific amount of
propellant.
The value of the heat of explosion of a composition may also be determined
through calculations. It is the result of the weighted algebraic sum of the
calorimetric values of its constituents (Section 4.1.).
4.4.3. A vail able range
This is primarily a function of the amounts of the major constituents
(nitroglycerine: 1750cal/g, nitrocellulose: 920cal/g, inert plasticizer: —1300
cal/g), as well as of the possibility of having a plateau effect. An increase in the
energetic level leads, in fact, to a decrease of the plateau effect, because of a
loss of efficiency of the combustion catalysts.
Today, the highest performances with acceptable ballistic characteristics
are approximately 1100 cal/g for EDB propellants and 900 cal/g for CDB
propellants.
An increase of the energetic level, significantly higher than these values,
may be obtained by adding nitramines (Chapter 11).
4.4.4. Correlation between the specific impulse
and the heat of explosion
There exists a linear relationship between the specific impulse and the
calorimetric value (Fig. 9). The difference between the theoretical specific
impulse and the delivered specific impulse for a reference rocket motor
weighing approximately 2 kg is about 15 s.
The weight of the reference grain is also an important parameter in terms of
influence. For instance, a difference of 2 s in specific impulse is found
depending on whether the measurement is made on a standard motor
equipped with a star-shaped central bore grain 203 mm in diameter, 500 mm
long, and weighing 19 kg; or with a grain measuring 90 mm in diameter,
300 mm in length, and weighing 2 kg.
Double-base Propellants
399
Fig. 9.9. Correlation diagram between the measured specific impulse, the theoretical
specific impulse, and the heat of explosion of double-base propellants.
5. Operating Characteristics
5.1. SIGNATURE
5.1.1. Smoke
Propellant combustion and the decomposition through pyrolysis of the
inert materials of the rocket motor (inhibitors and thermal insulation, for
example) generate smoke in the rocket exhaust which may have a detrimental
consequence, either by interference with the missile guidance or by permitting
the missile or its firing location to be revealed. A distinction must be made
between:
• primary smoke, which is generally the result of metallic particles con-
tained in the propellant; and
• secondary smoke, which may result from the condensation of the
combustion gases (H 2 0, for example) or of the combination of atmo-
spheric water vapor with certain combustion products (HC1, HF, and
others).
Various approaches, more or less quantitative, allow evaluation of the
amount of smoke produced by a propellant:
• thermodynamic calculation, used to determine the chemical products
resulting from the combustion;
• visual assessment; and
• optical measurements taken in the visible or the infrared wavelengths.
Homogeneous propellants produce no secondary smoke and little primary
smoke, since they contain no reducers and have only a small amount of
metallic particles from their additives [20] such as:
400 Herve Austruy
• ballistic modifiers, generally consisting of organic salts and copper or lead
minerals;
• particulate damping, generally consisting of refractory oxides, limited to
the necessary amount because they remain as solids in the jet and their
particle size can be optimized to reduce their interaction with light;
• Flash suppressant additives, which as alkaline-ion-based products
(usually potassium) may also include other metallic-type elements (alu-
minum, for instance).
5. 1.2. Secondary flame
Besides smoke, another element considered when assessing the signature is
the presence of flames in the exhaust. The combustion gases may re-ignite
downstream from the exit plane of the nozzle. This is known as the
afterburning phenomenon, which corresponds to an oxidation by the air of
the reducer products (H 2 and CO) produced by combustion of the propel-
lant.
Similar to the smoke, the measurement of the exhaust during propellant
combustion gives an indication of the intensity of the flash produced. The
signature is not limited to the visible spectrum, but occurs also in the infrared
region.
Many studies in this field have determined that the principal parameters
are:
• composition of the propellant (energetic level, combustion temperature,
nature of the gases, amount of reducing products, and presence of flash
suppressants);
• combustion conditions;
• performance of the missile.
To prevent secondary afterburning it is necessary to seed the exhaust with
particles likely to block the reactive mechanisms of re-ignition [22].
Many studies have been made to identify the additives that would be
effective and the best manufacturing processes. Among the products most
often mentioned in publications, and most widely used industrially, we find
products with an alkaline metal base (usually potassium), such as nitrate,
cryolite, sulfate, and potassium hydrogenotartrate, but also barium-based
and tungsten-based products. The selection of an additive is made by taking
into account not only its efficiency, but also the consequences resulting from
its introduction on the propellant performance, in particular:
• energetic level,
• chemical stability,
• aging properties,
• creation of primary smoke and
• ballistic performance.
Double-base Propellants
401
P(MPa)
Fig. 9.10. Diagram of burning rate-pressure of an E.D.B. propellant with and
without flash suppressant.
The direct introduction in manufacture during mixing of a flash suppres-
sant is likely to significantly modify the ballistic performance of EDB or CDB
propellants (Fig. 10); it is therefore necessary to modify the propellant
manufacturing process to avoid this problem.
In the case of EDB propellant it suffices to incorporate the flash suppres-
sant late in the process. This prevents it from mixing intimately with the
ballistic catalysts. By introducing the suppressant at the time of the final
rolling operation it is possible to obtain propellants with ballistic perfor-
mances which are not adversely affected by the presence of this additive.
In the case of cast double-base propellant the process modification consists
of separating the flash suppressant from the ballistic modifiers by using two
casting powders, only one of which contains the suppressant additive. This
allows the content of suppressant to be adjusted to the relative amounts of
the casting powders. The best trade-off needs to be determined between the
amount of additive in the special casting powder, and the amount of that
casting powder to be used in the composition.
5.2. COMBUSTION INSTABILITIES
5.2.1. Theoretical data
Under certain internal configurations and firing conditions, radial burning
grains may exhibit combustion instabilities that will translate into pressure
fluctuations. These instabilities may belong to two types:
• longitudinal instabilities, whose frequency is a function of the geometrical
dimensions of the grain (a few hundred hertz);
• high-frequency transverse instabilities, which may have two different
modes, radial or tangential, or possibly a mixture of the two.
402 Herve Au stray
These instabilities cause:
• perturbations in the nominal pressure, triggering oscillations of the thrust
delivered by the propellant grain;
• a possible pressure shift that may, in some cases, result in the extinction of
the grain;
• the risk of re-igniting the gas jet, leading to an afterburning phenomenon.
These instabilities are more frequently tiggered in propellants with a high
energy level or a fast burning rate.
5.2.2. Effect of the configuration of the
propellant grain and of the firing conditions
The frequencies of the instabilities are related to the geometrical dimen-
sions of the central bore of the grain. For instance, there usually is, for a given
diameter, a length above which combustion instabilities will occur (Fig. 11).
This length depends on the nature of the propellant. Conversely, for a specific
grain length these instabilities appear at a diameter smaller than a certain
limit value. We must also consider that, in addition to the length and the
diameter values, certain geometrical configurations of the central bore may
also be more prone to trigger instabilities. In the case of a star-shaped central
bore, for example, an even number of branches is a factor likely to trigger
instabilities (perfect symmetry of the grain).
While the firing conditions are a significant triggering factor, pressure is
still the essential parameter. While they do not occur at high operating
pressures, instabilities appear toward the lower pressure, generally corre-
sponding to the lower limit of the plateau effect. It is, as a matter of fact,
possible to identify a threshold pressure below which instabilities are started.
Similarly, low temperatures are more likely to trigger instabilities [22]. The
L/D
Fig. 9.1 1. Influence of the length of a 90 mm diameter star grain on the severity of the
combustion instabiliites.
Double-base Propellants 403
combination of a low pressure and low temperature (— 40°C) creates a high
likelihood of instabilities.
Finally, this phenomenon does not appear to be related to the chemical
nature of the propellant but rather to its ballistic characteristics (such as
burning rate), and its energetic characteristics (such as heat of explosion).
5.2.3. Function of the refractory additives
The presence of solid particles in the gas exhaust from the combustion
chamber permits damping of the pressure oscillations. A judicious selection
of their quality and quantity allows complete suppression of the combustion
instabilities (Fig. 12). There are several possibilities:
• a source, outside of the propellant, such as the inhibitor or the thermal
insulations, which, through degradation caused by the combustion, seeds
the gas exhaust with particles;
• the inclusion in the propellant of aluminum, zirconium, or tungsten
particles which, during combustion, produce liquid or solid products
(A1 2 0 3 , W 2 0 3 , for example);
• the presence of refractory additives in the propellant, which is the most
widely used technique.
The products used are selected on the basis of the smallest possible needed
quantity. Among the selection criteria are:
• The melting temperature, which must be greater than the flame tempera-
ture; the most widely used compositions are oxides (Zr0 2 , Si0 2 , B 2 0 3 ),
carbides (Si, Zr, Ti) and silicates (ZrSi0 4 ) [23].
Fig. 9.12. Evolution of the combustion instabilities recorded on an E.D.B. standard
ballistic grain (32 x 16 Type) as a function of the quantity of refractory additive.
404
Herve Austruy
• The particle size, selected in accordance with the formula:
where:
R = optimal radius of the particles,
fi = viscosity of the combustion gases,
p = density of the particles,
F = frequency of the instabilities.
In practice, the optimal radius is smaller than a micron.
• Finally, since these additives may have a detrimental effect on the other
characteristics of the propellant, they are chosen for the minimum
negative impact on:
— the chemical stability of the propellant and its energetic perfor-
mance,
— the burning rate and the temperature coefficient, and
— the signature.
5.3. EROSIVE COMBUSTION
Erosive combustion occurs when a solid propellant grain is exposed to a
gas flow, parallel to its surface and with a high flow rate (Q). We see a
significantly increased burning rate for the propellant ( V) compared with the
normal burning rate ( K 0 ), related by a formula of the type:
v = v Q ii + *(e-e.)]
where k is the erosivity coefficient of the composition (which depends on the
burning rate, the catalytic system used, etc.) and Q s the threshold of the flow
above which the erosive phenomenon occurs.
Firing of the propellant grain, followed by quenching, permits the analysis
of the contours, and determination of the erosivity coefficient. The erosivity
coefficient of EDB propellants is of the order of 4 x 10 “ 4 and the threshold
flow rate varies from 500 to 100 g per second per square centimeter.
6. Chemical Stability
6.1. BACKGROUND
The nitrate esters used with double-base propellants are molecules that are
not very chemically stable. In the usual ambient conditions of temperature,
pressure and hygrometry their decomposition is slow. However, in more
severe environments (high temperatures, acid chemical environment), the
Double-base Propellants
405
decomposition of nitric esters becomes autocatalytic. These reactions give
rise to radical thus:
rono 2 + ro 2 +no 2
The free radicals attack the nitrate esters not yet decomposed; this is followed
by a complex succession of secondary reactions producing gaseous products
such as CO, N 2 , and mainly, nitrogen oxides NO and N0 2 .
The function of stabilizers introduced into the propellant is to remove a
portion of the nitrogen oxides by fixing them chemically. The autocatalytic
procedure is thereby slowed down.
The stabilizer reactions involved correspond to a succession of nitrosation
and nitration reactions. In the case of 2-nitrodiphenylamine, it is of the type:
In these conditions the use of a double-base propellant is based on
knowledge of:
• the intrinsic chemical stability of the composition, assessed at the time of
its development and controlled during its manufacture;
• the preservation of sufficient stability for the entire service life of the
propellant, which is generally determined through the performance of
accelerated aging tests.
Consequently, the manufacturing controls are based mainly on two prin-
ciples:
• the inclusion of stabilizer in the propellant;
• the kinetics of emission of nitrogen oxides.
6.2. TESTS
6.2.1 . Stabilizer quantity
The inclusion of stabilizers is checked on standard samples that are
representative of the various batches. In the case of CDB propellants this
control is also made, on the casting powder.
406
Herve Austruy
The analyses are done using chromatographic techniques (chromatogra-
phy during the gaseous phase, or high-performance liquid chromatography).
The values obtained usually correspond to a theoretical percentage,
ranging from 1 % to 3 %. A drop in this percentage reveals a variation in the
manufacturing process such as, for example, a rolling temperature that is too
high.
6.2.2 . Stability test at 120°C
The high-temperature stability tests measure the rate of nitrogen oxide
output of a propellant standard specimen (2.5 g) placed in a test tube inside a
temperature-regulated enclosure. A methyl purple reactive paper is placed in
the tube. The color of the paper changes in the presence of nitrogen oxides.
This change of color marks the first release of nitrous vapors that are not
trapped by the stabilizer. The test usually takes place at 120°C in order to
accelerate the decomposition phenomenon and shorten the time necessary
for the paper to change color (a few tens of minutes). This type of test is also
done for CDB propellants, on the casting powder at 108.5°C.
The results obtained from these tests are a function of the compostion and
may vary for the double-base propellant family from 30 to more than
100 min. However, when testing a given propellant composition, industrially
manufactured, the values obtained are highly reproducible.
The results of these tests may not be directly related to the service life of the
propellant, but yet they allow us to assign each manufactured propellant a
reference value which is characteristic of the composition, thereby giving a
basis for detecting possible changes caused by foreign bodies in the propel-
lant, variation in manufacturing conditions, or quality of the raw material.
A significant difference in comparison to an average value indicates a
manufacturing deviation.
6. 2. 3. Chemiluminescence
This technique has been recently developed to assess the chemical stability
of propellants and to avoid some of the drawbacks of the test done at 120°C,
i.e.:
• 120°C is a very high temperature that is not related to the normal storage
temperature of propellant;
• the 120°C test is a global analysis of the phenomenon of the generation of
nitrogen oxides, without any distinction between the various types: NO,
N0 2 and others.
The chemiluminescence technique relates the amounts of NO and NO x to
the intensity of a luminous radiation that accompanies the chemical reaction
Double-base Propellants
407
(NO x : mixture of NO and N0 2 ) of NO in the presence of ozone.
NO + 0 3 ► N0 2 * + 0 2
N0 2 * ► N0 2 + hv
The quantity of light given out is directly proportional to the number of
nitrogen molecules contained in the gas being analyzed.
The propellant sample, when heated, gives off an amount of gaseous
nitrogen oxides. This gaseous sample is separated into two parts, one which
goes directly into a chamber containing ozone where the reaction takes place,
in front of a photomultiplicator, and the other first going through a catalytic
convertor that reduces NO x to NO.
The analysis of the data obtained in this manner allows us to measure by
deduction the amounts of NO, NO x and N0 2 . With this method the emission
of the various nitrogen oxides can be continually recorded.
A quantitative interpretation of this test for manufacturing control may be
done by specifying:
• the shape and weight of the reference sample;
• the temperature of the test;
• the duration of the test.
Finally, by comparing the NO and N0 2 levels, an indication of the degree of
the material alteration is obtained; the degree increases with the level of NO.
6.2.4. Other tests
The stability of propellants can also be measured by performing a number
of other gaseous evolution tests. These are generally done when there is a
need to determine the characteristics in a special environment. There is, for
example, the vacuum test designed to quantitatively measure the gaseous
volume released after a 200 h exposure to a specified temperature.
6.3. PARAMETERS AFFECTING THE CHEMICAL STABILITY [24]
Much work has been done to determine the parameters that have an
influence on the chemical stability of propellants. As a result, the following
parameters were identified:
• The heat of explosion', the increase in the energetic level results in an
acceleration of the kinetics of nitrogen oxide generation.
408
Herve Austruy
Heat of explostion
CDB Composition
Stability a 120°C (mn)
900 cal/g
Paste 1 + 2 NDPA
100
1 100 cal/g
Paste 2 + 2 NDPA
80
• The nature of the stabilizers :
Stabilizer Centra-
2 NDPA MNA Resor-
2 NDBA 1 % 2 NDPA 1 %
MNA 1 % Resorcinol 1 %
level 2% lite
cinol
Stability
at 120°C 60
(mn)
80 100 80
90 65
• The amount of stabilizers : with a llOOcal/g composition the stabilizer
does not have much effect at an amount above 2%.
• The nature of the additives'.
— potassium salts are usually detrimental to chemical stability;
— refractory additives have no influence;
— the effect of burning rate additives (Pb and Cu salts) depends on the
nature of the salt. Aromatic salts have the capability of fixing
nitrogen oxides, and are therefore generally favorable to chemical
stability.
7. Aging
The decomposition of the nitrate esters described above leads to an aging
of the propellant, depending on environmental conditions (temperature,
humidity, presence of inhibitor, etc.), resulting in the progressive consump-
tion of the stabilizer, which can culminate in a cracking of the propellant, an
alteration of the mechanical properties, and a change in the ballistic
properties.
7.1. CONSUMPTION OF THE STABILIZER
In order to assess the service life of a propellant in terms of its chemical
stability, samples are subjected to accelerated aging at temperatures ranging
between 60 and 80°C. The amount of stabilizer is measured over time. Based
on usual kinetic laws (Arrhenius or Berthelot), a stabilizer consumption law
can be deduced for the storage temperatures of the propellants.
With EDB and CDB propellants the service life that corresponds to a
consumption of less than 50% of the stabilizer is on the order of several tens
of years at ambient temperature.
Double-base Propellants
409
7.2. AGING-RELATED CRACKING
The gaseous products from the decomposition of the nitrate esters are
soluble in the propellant through which they diffuse to atmosphere. When the
kinetics of gaseous generation exceeds the rate of diffusion, the gases created
exert a pressure which may cause a physical breakdown of the material
(cracks, vacuum holes), particularly in the case of thick propellant grains.
Several formulas have been proposed to determine the critical pressure in
terms of the mechanical properties (S m , e m ) of the propellant [25].
The cracking phenomenon can be modeled, based on the laws:
• of Arrhenius for gas generation;
• of Henry for solubility of gases in propellant;
• and of Fick for gas diffusion.
The experimental studies may be done with propellant cubes, of different
sizes, subjected to high temperatures (on the order of 60-80°C). X-rays of the
cubes can detect the occurrence of defects such as vacuum holes and cracks.
This is known as the cube test. It can be used to determine the critical edge
length: the largest cube which, when subjected to a test of specified duration
at a specified temperature, exhibits no degradation [26].
The analysis of these results, extrapolated to normal temperatures, makes
it possible to determine the critical diameters of the grains of a given
propellant composition.
7.3. MECHANICAL AND BALLISTIC AGING
Providing that the environmental conditions are such that the chemical
stability of the propellant is preserved, double-base propellants do not have
any significant change of their mechanical or ballistic properties. However, a
substantial loss of nitroglycerine could lead to a hardening of the propellant.
8. Safety Characteristics
Propellant grains for rocket motors are designed and manufactured to be
used according to a well-defined decomposition mode: combustion burning.
This is a slow phenomenon that propagates itself through parallel layers. The
initiation of the phenomenon can be obtained through various types of
induced stress: thermal, mechanical, or electric.
However, propellant may, under certain conditions best avoided, adopt a
different mode of decomposition, even a different regime of decomposition.
410 Herve Austruy
8.1. SAFETY AND TOXICITY OF THE INGREDIENTS
The various ingredients used in propellants are indexed in toxicity lists
which indicate the various and particular precautions that must be observed
during the manufacture.
As far as the pyrotechnic safety characteristics are concerned, the nitrocel-
lulose is usually desensitized through the addition of water — manufacture of
pastes — or alcohol. (A propellant conditioned with alcohol belongs in the
hazard class 1.4.)
On the other hand, taking into account its characteristics (Table 4)
nitroglycerine is never used pure, but in association with nitrocellulose (EDB
propellant pastes) or with triacetin, a casting solvent for CDB propellants.
The crystallization of nitroglycerine, likely to occur at temperatures below
12°C, must be prevented, although the crystallized product is no more
sensitive than the liquid product. The hazard lies in the fact that the
crystallization is likely to produce frictions between the crystals, and thus in
turn may lead to a decomposition by detonation.
In addition to the pyrotechnic risk, nitroglycerine is also toxic. Its vapors
cause migraines and nausea because it is a cardiac hypotensor.
Table 4 Comparison of safety characteristics between nitroglycerine and casting solvent
Test
Results
expressed in
Nitroglycerine
Casting solvent
(78% Nitroglycerine)
Card gap test
Number of cards
>340
75
Sensitivity to 30 kg
fall hammer
Height of no
reaction (m)
0.5
>4
Critical thickness
mm
<0.1
4
Steel tube-drop test
Height of no
reaction (m)
<0.25
1
8.2. APTITUDE TO IGNITION
8.2 . 1. Heat sensitivity
The heat sensitivity tests are designed to determine the temperatures at
which a propellant specimen ignites. These tests may be performed with
specimens broken into small pieces (autoignition test) or compact (cook-off
test).
8. 2. 1.1. A uto ignition test
This test is used to measure the temperature of spontaneous ignition of the
propellant:
Double-base Propellants 411
• either by progressive heating, regularly increasing the temperature by 5°C
every minute;
• or by sudden heating.
These tests tell us exactly the maximum temperatures to which the propellant
can be subjected during its manufacture or its use.
In the progressive heating test, 180°C is a reference temperature used for all
double-base propellants.
8.2. 1.2. Cook-off test
This test is used to determine the lowest temperature of spontaneous
ignition after extended exposure to that temperature.
This temperature is around 110°C for all double-base propellants.
8.2.2 . Mechanical sensitivity
The combustion of the propellant may also be triggered by the mechanical
stimuli of impact or friction. Various tests have been devised to quantify the
level of stimulus necessary to cause ignition, including:
• friction sensitivity: the average recorded value is of the order of 20
Newton;
• impact sensitivity.
Several tests have been developed to characterize the impact behavior of
propellants. Two of these are most widely used:
• the 30 kg fall hammer test: the principle involves dropping a 30 kg weight
onto a plate of propellant; the height of the drop determines the amount
of energy involved;
• the impact sensitivity test: steel fall hammers of various weights are
dropped from varying heights onto a propellant sample held between two
steel clamps.
The values obtained in these tests identify the level of impact that are
prohibited for the propellant (dropping propellant grains, shocks, etc.).
8.2.3. Electric sensitivity
Double-base propellants have been found insensitive to electric energy up
to about 600 mJ.
8.3. DETONABILITY
Detonation is an exothermic chemical decomposition reaction which,
coupled to a shock wave, propagates itself through the material. This
412
Herve Austruy
accidental rate of decomposition is a risk for all solid propellants, and in
particular for double-base propellants. A certain number of criteria exists
that permits us to characterize the detonability:
• the detonability index. When compared to the results obtained with
composite propellants — one card — the values corresponding to double-
base reveal a significantly increased aptitude for detonation: 90-100
cards.
• the critical diameter. They are significantly smaller than those of compo-
site propellants.
Table 5 provides an overview of the major safety characteristics of double-
base propellants.
Table 5 Main safety characteristics of double base propellants ( typical cases)
Tests
1000 cal/g EDB
800 cal/g CDB
Ignition
Autoignition through progressive heating
173°C
176°C
Autoignition through sudden heating
268°C
277°C
Cook-off
1 10C
Friction sensitivity
210 N
210 N
30 kg hammer fall sensitivity (no reaction)
greater than 4 m
greater than 4 m
Impact sensitivity
4.9 J
5.9 J
Static electricity sensitivity
600 mj
600 mJ
Detonability
Card gap test
100 cards
90 cards
Critical diameter
2 mm
14 mm
Bibliography
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Contribution a I’etude des interactions entre les nitrocelluloses et la nitroglycerine. Compar-
aison de cette derniere avec differents solvants. 1969.
2. Cosgrove, J. D., Hurdley, T. G., Lewis, T. J. and Perme, W. A., The diffusion of acetone
and isopropyl nitrate into nitrocellulose and nitrocellulose/nitroglycerin in films. Conference
on Nitrocellulose Characterisation and Double-Base Propellant Structure. Waltham Abbey,
Essex, England, 1980.
3. Quinchon, J. and Tranchant, J., Les Poudres , propergols et explosifs. Tome 2: Les
Nitrocelluloses et autres matter es de base des poudres et propergols . Editions Lavoisier,
Technique et Documentation, 1984.
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combustion — Migration a travers les vernis polyesters. Universite de Bordeaux I., 1976.
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moulage a chaud des blocs de propergol double-base, 1976.
9. Craig-Johnson, C. E. and Dendor, P. F. No roll process for manufacture of double-base
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10. Gimler, J. R., Solventless extrusion of double-base propellant prepared by a slurry process.
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11. Muller, D. and Stewart, J., Twin screw extrusion for the production of stick propellants.
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16. Charre, J. M., Longevialle, Y. and Naideau, P., Test de pertes de charges. Application a
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CHAPTER 10
Composite Propellants
ALAIN DAVENAS
1. Introduction
Composite propellants are made of a polymeric matrix, loaded with a solid
powder oxidizer, and possibly a metal powder that plays the role of a
secondary fuel component.
In composites the oxidizing and reducing atoms are not in the same
molecule, as is the case with double-base propellants, thereby creating a
microscopically homogeneous phase, but are rather juxtaposed with a
composite structure. A certain number of properties, such as burning rate,
rheology, and mechanical behavior, are directly related to this composite
character.
The first composite propellants used thermoplastic binders such as asphalt,
polyvinyl chloride, and polyisobutylene. Their use required softening or
melting obtained through a temperature increase. Around 1950, the first
liquid binders allowing crosslinking appeared. Because these binders allowed
high ratios of oxidizing and fuel charges, they led to the considerable
development of composite propellants in large case-bonded grains (several
tens of tons, even several hundreds of tons of propellant) that were impossible
to manufacture with other types of propellants.
This development era can be broken down into two major periods:
• From 1950 until 1965, when composite propellants were made with
polysulfide binders (“thiokols”) and with polyurethane polyethers.
• From 1965 on, new binders emerged, with a functional polybutadiene
basis: acrylonitrile-acrylic acid-butadiene, acrylic acid-butadiene co-
polymers, and homopolymers with functional ends called telechelics.
These new polymers led to increasingly better-performing elastomer
binders, since they offered higher solids loadings and a wider operating
temperature range, especially at low temperatures.
Clearly the significant events in the history of composite propellants are
tied to the emergence of high-performance binders and not to new oxidizers.
415
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Alain Davenas
Indeed, although ammonium perchlorate was not used right away — first
potassium perchlorate and ammonium nitrate were used — it rapidly became
the oxidizer of choice.
2. Formulation of Composite Propellants
Like all solid propellants, a composite propellant must produce hot gases
which create a thrust by expanding in the nozzle, and include an oxidizer-fuel
couple with a reaction capable of releasing sufficient energy to ensure the
burning of the grain.
Oxidizing and fuel products come in the form of solid powders, which must
be incorporated into a binder to give cohesion and homogeneity. This binder
must exhibit very specific properties:
• It must be in liquid form during the preliminary phase of the preparation
of the intimate mixture of the oxidizer and the fuel charge, although its
elements must have sufficiently low volatile characteristics to withstand
the high vacuum used during the mixing of the slurry and the casting into
a grain.
• It must be chemically compatible with the oxidizer, which means that it
will not cause even a slight temperature increase that would result in an
exothermal reaction causing an unwanted autoignition of the propellant.
• It must be capable of accepting very high solid loading ratios (up to 80%
in volume). The mixing operation must remain feasible, and the resulting
slurry must be easily cast into a molding system or into the case of a
rocket motor with molding devices with shapes that are often complex
and include some fairly narrow sections.
• After the slurry is in the mold, crosslinking must ensure its transforma-
tion into a solid through a chemical reaction obeying the following
criteria:
— It must be a polyaddition reaction. Any elimination reaction produc-
ing more or less volatile products would result in the creation of
cracks or “bubbles” in the crosslinked mass. Additionally, the
mixing of the slurry must be done under vacuum to eliminate the gas
present in soluble form in the binder. The decrease of the solubility of
the gases during the crosslinking would lead to cracks in the
propellant during cure.
— This reaction must have on one hand a sufficiently slow cure kinetic
to allow for the casting operations — this useful reaction time of
several hours is also known as “pot-life” — and on the other hand
must set sufficiently rapidly so as not to require lengthy crosslinking
or curing times.
The curing temperature cannot be too high, so as to prevent severe
mechanical loads in case-bonded propellants.
Composite Propellants
417
— It must also be athermic, or not very exothermic, to avoid the release
of heat inside the grain, resulting in an increase of temperature inside
this material, which is a poor heat conductor. This temperature
increase could lead to mechanical loading conditions, possibly
leading to cracks and autoignition of the propellant.
• Finally, once it is cured, the binder must lend its mechanical properties to
the propellant.
Case-bonded grains are used in most of the composite propellants applica-
tions, i.e. the propellant forms one piece with the structure through the use of
a bonding material, the liner. During its service life the propellant is subjected
to major thermal stresses, resulting in significant strains because the thermal
expansion coefficient of composite propellants is approximately ten times
greater than that of the metals or composite materials used to make the cases.
At firing, the propellant is, in addition, subjected to a range of important
stresses and strains due to the deformation of the case under pressure.
The cured propellant must be able to withstand these strains without
rupture, requiring it to have elastic type properties, viscoelastic to be more
precise. These properties can only be provided to the propellant by the
binder, which, taking into account the high proportion of solid loading, must
therefore be an excellent elastomer. It is not unusual to require strains of 50%
from the propellant, which means that the strains are more than ten times
greater for the binder.
In Fig. 1 the tensile strength of a binder is compared to that of a propellant
with a solid loading ratio of 88%. This figure demonstrates the effect of the
loading ratio on the tensile strength (multiplied by 5) and on the strain at
rupture (divided by 8) for a polybutadiene-AP-Al propellant.
1 . 88% solids
2. Pure binder
Fig. 10.1. Stress-strain curves.
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2.1. THE BINDER
The binder is essentially composed of a liquid prepolymer, with chemical
capability to react with a crosslinking system designed to ensure the
dimensional stability of the product after the reaction has taken place.
In simplified terms, a prepolymer is a molecule formed by the repetition
(several tens of times) of a monomer form (butadiene, polypropylene oxide,
etc.), generally ending with reactive functions (telechelic prepolymers).
The crosslinking system may in its most simple state be a polyfunctional
molecule (at least trifunctional) with a low molar weight, or a mixture of
difunctional molecules, called chain extenders, whose role is to increase the
length of the chain of prepolymers and of at-least-trifunctional molecules in
order to ensure an average functionality (number of reactive functions,
divided by the total number of molecules) greater than 2 for the whole
crosslinking system.
After the polyaddition, chemical reaction has occurred between the pre-
polymer and the crosslinking system and the three-dimensional links are
created. If they are in sufficient number — in the areas where it is not
glassy — the resulting binder has a vulcanized elastomer type of behavior.
The crosslinked density of a binder, as well as the molecular mass between
two links, are the essential characteristics of the network that constitutes the
binder. These characteristics determine, in particular, its mechanical proper-
ties.
Many attempts have been made to link the mechanical properties (repre-
sented by the elasticity modulus) of the crosslinked polymer to the structure
of the network defined by the crosslinking density and the molecular mass
between two links (from 10,000 to 100,000 in usual composite propellants).
They all derive from the statistical theory of rubber elasticity which links
strain and stress according to:
where: o = kT(<x — oe“ *)
o stress;
k Boltzman constant;
T absolute temperature in K;
a relative deformation of the specimen;
v number of segments between links
where v = p/M c N and E — vkT
p mass per unit volume of the polymer;
N Avogrado number;
M c molecular mass between two links;
E elastic modulus.
In reality this formula does not apply very well, because the binders of
propellants are viscoelastic. It is useful only after long periods of relaxation,
when there is equilibrium or quasi-equilibrium.
Composite Propellants
419
To be freed from this complication, M c measurements are done on
specimens swollen in a solvent. The Flory-Rehner theory [1] allows us then
to determine the mass between links.
Finally, it is necessary to discuss the kinetics of crosslinking in order to
describe the formation of the network on which the development of the
rheologic characteristics of the slurry will depend.
Theories have been formulated based on the observation of the probability
of reaction at the reactive sites [2]. Unfortunately, all of these theories come
up against the complexity of the reactional system, whose exact characteris-
tics are difficult to assess, such as: distribution of molecular masses and
functionalities of the prepolymer; reactivity of the reaction sites which change
during the formation of the network, and in particular, difficulty in measuring
the development of reactive functions after the gel point where, through the
formation of the first “infinite” molecule, the reacted group becomes partially
insoluble. The use of these theories is nevertheless essential in guiding
propellant designers.
2.1.1 . Prepolymers
Prepolymers are the main element of the binder of composite propellants
(70-80%). It is the prepolymer that confers on the binder its essential
properties. These can be derived from the nature of the polymeric chain or the
properties of the functional ends.
2. 7. 7. 7. Characteristics related to the chain
Several examples are given in Table 1.
(a) A H fo Enthalpy of formation
The higher this quantity is, the more energetic it will help make the
propellant (in fact, less negative, because for all usual binders A H fo is
negative).
This enthalpy is directly related to the nature of the links between the
atoms of the chain, which typically are C, H, O and N.
We will see, later in this chapter, that the binder must consist of light atoms
which, through their combustion, will produce gases leading to a high specific
impulse.
(b) Oxygen content
It would actually be better to talk about the ratio of the oxidizing valences
(O, F, Cl) versus the reducing valences (C, H). In practice, the binders used so
far contain, with a few exceptions, only C, H, O and N. Under these
Table 1 Properties of the polymers used in composite propellants
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Glass transition temperature measured by performing a differential enthalpic analysis.
= Weight average molecular weight.
Composite Propellants
421
conditions it seems logical to assume that only the oxygen present in the
binder counts as oxidizing valences, and it is customary to consider the mass
percentage of the oxygen in the binder. The higher this percentage, the less
necessary it is to use high levels of oxidizer to obtain the maximum specific
impulse. We must note, however, that the optimum does not correspond to a
complete combustion of the reducing valences, as we will see later.
However, the incorporation of high ratios of oxygen in the binder through
ether, ester, or carbonate functions is accompanied by a decrease of the
enthalpy of formation. This is the reason why there is little interest in these
types of binders, except for special applications, such as “cold” propellants or
when plasticized by energetic molecules. This is especially true since other
parameters intervene adversely: increasing glass transition temperature, and
decreasing capability to withstand high solid loading when the amount of
oxygen increases.
In practice the polybutadiene chain offers a good energetic compromise in
spite of a density somewhat lower that that of oxygenated binders (Fig. 2).
Fig, 10.2. Theoretical specific impulse as a function of AP concentration for three
types of prepolymers.
(c) T , Glass transition temperature
This transition point of the second order corresponds to an important
modification of the mobility of the polymeric chain that occurs when the
temperature decreases and goes through a phase called “glass transition”,
which spreads over approximately 10 degrees Celsius. The physical proper-
ties of the polymer are greatly modified. Its elasticity modulus, in particular,
increases significantly, and the capability of elongation becomes very small:
the polymer has lost the specific qualities for which it was used. Table 1
shows, again, the advantage of using polybutadiene, at least for structures
including no more than 20% of vinyl groups.
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(d) Average molecular weight
The average molecular weight is tied to the number of monomer units
which make up the prepopolymer chain — a few tens of units for the
polyethers and polybutadienes — and therefore to the length of the segments
of the macromolecular network. Therefore, it plays an important role in:
• The average molecular weight between links in the binder, i.e. its
mechanical properties (low masses lead to a highly crosslinked and very
rigid network).
• The viscosity of the propellant slurry. The slurry may not exceed a certain
viscosity of the order of 15,000 to 20,000 poises if the filling of the molds is
to occur under good conditions using classic processes. The viscosity of
the prepolymer, which is the main element of the binder, may not exceed
certain values. In practice it varies from a few tens of poises to a few
hundreds at 25°C.
Beyond that, it is virtually impossible to do the mixing under good conditions
without using extremely large quantities of plasticizer, which may lead to
undesirable changes in aging properties.
Below several poises the molar mass of the prepolymer is usually too low,
and the resulting network will be too rigid.
(e) Polydispersity index, / = /W p //W n
Ratio of the weight average molecular weight versus number average
molecular weight, this characterizes the distribution of the molecular weights
around the average weight and is, consequently, related to the structure of the
network (distribution of the molecular weight between the links). In Fig. 3 the
Fig. 10.3. Molecular weight and functionality distribution of an HTPB pre-
polymer.
Composite Propellants 423
distribution curve in weight of a hydroxytelechelic polybutadiene (HTPB) is
given as an example.
2. 7. 1.2. Characteristics related to the functional ends
We have already seen that the functionality — the number of reactive
functions per molecule — should be at least two to ensure a good formation
of the network. This condition has been proven correct for many of the
polymers in Table 1.
We must however mention the average functionality of 2.2 to 2.4 for HTPB
R45M, which indicates a mixture of molecules with variable functionalities
(from 0 to 7). This is related to the synthesis process of this polymer [3], and
it has not been an obstacle to its development since 1970.
Ideally, the reactive functions should be located at the end of the chain to
take advantage of its entire length and mobility.
In practice, the ends most widely used are the hydroxyl and carboxyl
(hydroxy or carboxytelechelic polymers) whose methods of crosslinking are
indicated in Table 2.
2.1.2. The crosslinking agent
As discussed, the function of the crosslinking agent is to bind the
prepolymer molecules and is, when the functionality of the prepolymer is 2, to
lead to the crosslinking nodes of the network. Therefore it plays a critical role
in the crosslinking kinetic and in the mechanical properties of the propellant.
There are three types of polyaddition reactions used for solid propellants:
• Addition of an alcohol to an isocyanate. Isocyanates R l — N=C=0
react with most of alcohols R 2 — OH according to the reaction:
Ri — NC=0 + R 2 — OH > Ri — NH — C — O — R 2
ii
o
The link NH — C — O is called urethane.
II
O
• Addition of an organic acid to an epoxide
R.—C— OH + R 2 — C— CH 2 -► R, — C — O — CH 2 — CHOH — R 2
II \ / II
o o
o
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Table 2 Crosslinking systems for prepolymers
Nature of the
ends of prepolymers
Crosslinking
system
Functions
created
Hydroxyl
(polybutadiene.
Triol + diisocyanates
Urethane
polyester
polyoxypropylene)
Ex: TMP a + TDI b
— O— C— N—
II II
O H
Carboxyl
(polybutadiene,
1. Polyepoxide
Alcohol ester
polyester)
Ex.: Epon 812 c
from Shell
2. Polyaziridine
Ex.: MAPO d
— c— o— CH 2 — CH—
II 1
O OH
Ester amine
— c— O— CH 2 — CH —
ii i
o nh 2
a TMP = Trimethylol propane
ch 2 oh
\
ch 3 — ch 2 — c— ch 2 oh
ch 2 oh
b TDI = Toluylene diisocyanate
O
Composite Propellants 425
• Addition of an organic acid to an azidirine
R, — C — OH 4- R 2 — C — CH 2 - Rj — C — O — CH 2 — CH — R 2
II \ / II I
O NO NH2
I
H
(a) Effect on the mechanical properties
Figure 4 gives an example of the important effects of the stoichiometry, and
of the percentage of crosslinking agent on the mechanical properties of a
polybutadiene-AP-Al propellant. We must note that below a certain level of
crosslinking (in this case, 0, 94 for the curing ratio), the propellant is not
sufficiently crosslinked. Beyond this limit, maximum strains and stresses
increase, which is a very general behavior of these compositions.
(b) Influence on the kinetic of polymerization
The reactivity of the crosslinking functions versus the prepolymer func-
tions must be properly selected. Polyoxypropyleneglycol with secondary
hydroxyl functions, for instance, requires an aromatic isocyanate that is fairly
reactive (such as TDI), while R45M with primary hydroxyl ends is to be
crosslinked with an aliphatic or cycloaliphatic diisocyanate that is less
reactive, isophorone diisocyanate (IPDI), for example.
2.1.3. Plasticizer
Plasticizer plays the essential role of complementary element to reduce the
viscosity of the slurry, therefore facilitating production, and to affect the
mechanical properties by lowering T g and the modulus of the binder.
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Typically, it is an oil that is non-reactive with the polymer, a true diluting
agent whose function is to separate the polymer chains, thereby reducing
their interaction in the liquid state as well as in the crosslinked state. Table 3
lists the major plasticizers (polyesters for the most part) and Table 4 shows
the effect of a plasticizer on T g . Plasticizers contribute to lowering the mix
viscosity and extending the elastic range at low temperatures. However, they
have the drawbacks of being able to migrate, particularly at the propellant-
liner and/or propellant-inhibitor interfaces, thereby modifying the properties
of the propellants in those areas.
Table 3
Diisoocytyl azelate
Major plasticizers for composite propellants
COO— C 8 H 17
Diisoctyl sebacate
Isodecyl pelargonate
Polyisobutylene
Dioctyl phthalate
(CH 2 ) 7
coo— c 8 h 17
coo— c 8 h 17
^ coo— c 8 h 17
ch 3 (CH 2 ) 7 coo c 10 h 21
(CH 2 ) 8
/\
c O C g H , 7
o
-c-o-c 8 h 17
o
Table 4 Influence of the percentage of plasticizer on r g of a poly ether 4- diisooctyl azelate
binder
Plasticizer/polyether (%) 0 10 30 50 70 100
TfC -68 -75 -80 -85 -101 -107
2.1.4. Additives
These are liquid or solid products added at a few percent of the binder.
Their function is to modify at will the characteristics of the propellant to
improve them, except specific impulse, which they often decrease due to
secondary adverse effects. This decrease does not exceed 1-2%.
Composite Propellants
427
2. 1.4. 1. Burning rate modifiers
These are used to modify the propellant burning rate — beyond what can
be done with variations of the particle size of the solids — and to adjust the
exponent “n” of the burning rate-pressure curve in the pressure zone where
the propellant grain will be operating.
There are two types of burning rate modifiers: accelerators and modera-
tors.
(a) Burning rate accelerators
These are products that accelerate the decomposition of the perchlorate, or
that lower its decomposition temperature. Virtually all burning rate accelera-
tors are mineral or organic metallic by-products of copper, iron, chromium,
or boron.
For many years only solids, iron oxides, and copper chromite were used.
Liquid derivatives from iron (ferrocene derivatives) and boron (carboranes)
are also used because their incorporation as plasticizers to the binders
facilitates the high amounts necessary for high burning rates without
lowering the loading ratio of energetic solid charges. The major ferrocene
derivatives in use are listed in Table 5.
Unfortunately, because they are not linked with the network, these
products, like the plasticizers, have a tendency to migrate at the interfaces.
That is why we are now trying to graft the useful functions to the basic
polymer chain. Prepolymers resulting from the addition of sililferrocene onto
functional polybutadiene vinyl groups are currently being developed [4].
The curves shown in Fig. 5 illustrate the effect of a solid burning rate
Table 5 Major ferrocene derivatives used as burning rate accelerators
Ferrocene (Fe)
n-Butylferrocene
Di n-butylferrocene
Catocene
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20
i n 1 i i i i i i i—i i i i i 1 — i — i — ►
1 2 3 4 5 6 7 8 910 20 30 40 506070
P(MPa)
Fig. 10.5. Burning rate vs pressure curves for propellants with burning rate accelera-
tors.
accelerator (copper salt) and a liquid one (ferrocene derivative) on polybuta-
diene-AP-Al propellants.
The efficiency of burning rate accelerators is highly dependent on the
nature of the oxidizer. While there is a large number of burning rate modifiers
for ammonium perchlorate and ammonium nitrate propellants, they are
rather rare for potassium perchlorate composite propellants, or composite
propellants that use organic energetic solids such as HMX or RDX.
(b) Burning rate moderators
There are two types of moderators, based on their mode of intervention.
Additives modifying the kinetic of decomposition of ammonium perchlorate.
These generally are alkaline salts, or alkaline-earth solids added in low
proportions, not exceeding 1-2% of the propellant.
Like the burning rate accelerators, although to a lesser degree, their
efficiency varies as a function of the pressure, and is also associated with a
decrease of the pressure exponent. Figure 6 gives an example of the effect of
lithium fluoride on an ammonium perchlorate propellant. Although the effect
of these additives could be significant (lowering of the burning rate by 50%),
very slow burning rates cannot be obtained. Furthermore, they have no effect
on aluminized propellants. As a result, “coolants” are preferred.
Coolants , also called “cold oxidizers,” are products that also lower the
propellant burning temperature, and unfortunately, its specific impulse as
well, by:
• a lowering of A H {o , while maintaining a high content of oxygen;
• enriching the combustion gases with nitrogen which, since it takes no part
in the combustion, acts as a diluter.
Composite Propellants
429
Fig. 10.6. Effect of lithium fluoride on the burning rate of an AP composite
propellant.
The more commonly used coolants are:
• oxamide NH 2 — C— C — NH 2 ;
ii ii
o o
• nitroguanidine NH 2 — C — NHN0 2 ;
NH
• ammonium nitrate.
Their main properties are listed in Table 6.
Oxamide has the most severe adverse effect on the specific impulse, but it is
also the most efficient of the coolants. In practice, ammonium nitrate is used
mainly as the major oxidizer for propellant with very low burning rates (but
not very energetic) ranging from 1 to 2 mm/s at 7 MPa.
These products make it possible to reduce by half the burning rate of
Table 6 Some characteristics of the major coolants
Coolant
0(%)
N (%)
Density (g/cm 3 )
A H !c (kcal/kg)
Nitroguanidine
30.7
54
1.76
-217
Ammonium nitrate
60
35
1.72
-1090
Oxamide
36
31.8
1.67
-1355
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ammonium perchlorate propellants, including those that are aluminized,
with a drop in specific impulse up to 10 s.
2. 7.4.2. Surface agents and binder-charge bonding agents
For many years the only role of these additives, used in low quantities not
exceeding 1% of the binder, was to help the manufacturing of the propellant
by decreasing the viscosity of the slurry. In this capacity all surface agents
that decrease the surface energy of the solid charge, to permit better
“wetting” of the surface by the binder, can be used.
However, it was quickly noticed that these agents, as valuable as they may
have been in terms of the production, had a detrimental effect on the
mechanical properties of the propellant by preventing the adhesion of the
binder to the solids, thereby decreasing its tensile strength. Consequently,
products called bonding agents have been developed, which through a
judicious adaptation of their molecules, of the formulation of the binder, and
of the mixing process of the ingredients play a double role, serving as wetting
agent for the solids and increasing the cohesion between the binder and the
solids [5].
A good bonding agent must satisfy the following criteria:
• Be efficient at very low levels (less than 1%).
• Be capable of bonding itself on a solid (generally the oxidizer, because it is
the most important ingredient in terms of quantity). As a result, a
bonding agent is specific to the type of solid.
• Be capable of incorporating itself with the binder through a chemical
reaction which must be compatible with the crosslinking system.
• Reinforce the mechanical properties of the binder in the vicinity of the
solids where the highest mechanical stresses appear in the area close to
the surface of the charges [6].
Triethanolamine is a good example of a bonding agent for ammonium
perchlorate in poly urethane- type binders through:
• Reaction on the surface of the perchlorate by displacing the ammonia and
forming triethanolamine perchlorate.
• Integration in the binder through the highly reactive primary alcohols.
• Trifunctionality of the molecule, ensuring a good crosslinking density in
the area close to the ammonium perchlorate particles.
Because of the release of ammonia with amine-type bonding agents, polyazir-
idine-type additives are often preferred. Several of these additives are listed in
Table 7. A good example of this family of additives is MAPO, which
polymerizes on contact with ammonium perchlorate by opening aziridine
rings. This layer becomes reactive to isocyanates, as illustrated in Fig. 7.
Composite Propellants
Table 7 Binder-solid bonding agents: imine or aziridine type
431
MAPO
HX 752
MT4
Methyl BAPO
Tri (2-methyl- 1-aziridinyl) phosphine oxide
Bis-isophtaloyl-l-methyl-2-aziridine
Product resulting from the reaction of 2 MAPO moles: 0.7
adipic acid moles and 0.3 tartric acid moles
Methylamino-bis (2-methyl-l-aziridinyl)-phosphine-oxide
HTPB Hydroxylterminated polybutadiene
DOA Dioctyl adipate
IPDI Isophorone diisocyanate
Fig. 10.7. Reaction of MAPO with IPDI and HTPB.
A number of additives featuring nitrile groups are also fairly widely
used [8].
2. 1 .4.3. Catalysts
Catalysts are often necessary to reduce the curing time of the propellant.
Besides the kinetic aspect they may have a significant impact on the
mechanical properties by facilitating some favorable reactions, thereby giving
direction to the formation of the polymer network.
They are usually organic salts of transition metals (iron, chromium, tin).
Several examples are provided in Table 8. Very detailed research is being
performed because their nature and the amounts used must result in a trade-
off between the workability of the mixture (viscosity of the slurry, pot life),
curing time, and mechanical properties.
Complex systems with two or three chemical products such as triphenyl-
bismuth, maleic anhydride, and magnesium oxide have emerged, and allow
excellent compromises between pot life and curing time [9].
432 Alain Davenas
Table 8 Catalysts for polyurethane binder propellants
Iron acetyl acetonate
Fe(C 5 H,0 2 ) 3
Copper acetyl acetonate
Cu(C 5 H 7 0 2 ) 2
Lead octoate
[CH 3 — (CH 2 ) 3 — CH— COO] 2 Pb
c 2 h 5
Ditubyl tin dilaurate
CH 3 — (CH 2 ),o— coo c 4 h 9
\ /
Sn
/ \
CH 3 — (CH 2 ) i0 — coo c 4 h 9
Lead chromate
Pb CrO*
2. 1.5. Various additives
Based on the various properties required from the propellants, specific
additives are included. These usually are solids and their amount rarely
exceeds a few percent of the binder.
2.1 .5.1 . Antioxidant
These are essential to ensure satisfactory aging of the propellant in various
ambient conditions.
The binder, an organic material, is subject to degradations that are
reflected by changes in the network and consequently, in the mechanical
properties of the propellant. Generally, the combustion properties are little
affected.
The aging may be:
• Oxidizing: this occurs with either the oxygen in the surroundings of the
propellant grain, or gases occluded inside the propellant. Antioxidants
are added, usually phenols or aromatic amines. This occurs particularly
in the case of propellants with polybutadiene binder, whose C=C links
are particularly sensitive to oxidation, in accordance with mechanisms
that have been extensively studied for high molecular mass rubber.
Antioxidants, well known in the rubber industry, are used, phenols in
particular (di tertiary butyl paracresol, diamino n-phenyl-n'cyclohexyl-
paraphenylene, 2.2. methylene bis (4-methyl-6-tertiary-butyl phenol),
among others).
• Hydrolytic: this occurs with polyesters, where the ester links may
hydrolyze and lead to a depolymerization of the binder.
Composite Propellants
433
2. 7.5.2. Burning rate stabilizing agents
The pressure-time curve of a propellant grain may be considerably
disturbed by inopportune local variations in the burning rate of the propel-
lant. This is often the case with non-metallized propellants.
Based on the origin of these disturbances, the grain designer uses stabiliz-
ing additives of a varying chemical nature:
• Opacifiers (carbon black): these are found to be necessary in non-
metallized propellants to block the radiation of the burning front, which
has a tendency to heat the propellant below the burning surface,
accelerating its combustion and creating low pressure fluctuations.
• Anti-instabilities and damping additives: these additives are discussed in
Chapters 4 and 5. Their use may eventually adversely affect the polymeri-
zation of the propellant.
2.2. SOLIDS
There are two types:
• Oxidizers: the primary ingredient of the propellant (60-80%).
• Fuels: generally used in amounts not exceeding 25%.
These are powder solids whose shape and particle size determine the
maximum amounts that can be included in the binder [11]. Figure 8 shows
the influence on the relative viscosity (ratio of the viscosity of the suspension
versus the viscosity of the interstitial liquids) of several particle size distribu-
tions of spherical particles whose diameters range between a 5 to 10 ratio. For
a given viscosity limit (imposed by manufacturing capabilities), the accept-
Distribution
* Monomodal
□ Bimodal
O Trimodal
o Tetramodal
• Octomodal
x Infinite modal
0.4 0.6 0.8
Percentage of solids by volume
Fig. 10.8. Comparison of relative viscosities calculated for multimodal optimum
systems.
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able amount of charges by volume increases with the number of particle sizes,
each particle size settling in the gaps formed by the larger sizes.
Three or four particle sizes are commonly used in propellants; it is
sufficient to come close to a viscosity optimum for a specific solid loading.
However, it is not always possible to use the particle size distribution best
suited to obtain a high solid loading. This is due to the fact that particle size
has a considerable effect on the burning rate of the propellant, and often it is
this parameter which predetermines the size of the particles that will be used.
The nature of these solids is, of course, the major parameter influencing the
energy of the system, although it also affects the burning rate, as already
discussed.
In Chapter 1 we saw that the specific impulse can be expressed in a very
simple manner:
where:
T c = combustion temperature in the chamber;
M = average molecular weight of the exhaust gases.
The selection of an oxidizer-fuel couple is consequently a compromise
between seeking to obtain a high burning temperature (related, in prelimin-
ary analysis, to the enthalpy of the formation H fo of the propellant), a low
molecular weight for the combustion products, a high propellant density and,
naturally, the required burning rate.
2.2.1. Oxidizers
The characteristics of a good oxidizer are:
• The capability of supplying oxygen (or fluorine) to burn the binder and
the other fuel, with the maximum heat of combustion.
• The highest possible formation enthalpy. Figure 9 shows the formation
enthalpies of the major kinds of oxidizer products that include the
groups: C10 3 , C10 4 NO s in the solid products.
The advantage of using NF 2 and N0 2 is revealed by the good location in
the graph of CH 3 N0 2 , N 2 F 4 :
• The highest possible density.
• A sufficient thermal stability. Decomposition temperatures exceeding
100°C are required to permit the manufacturing operations and to
safeguard the propellant.
• A good chemical compatibility with the other ingredients contained in
the propellant, in order to avoid any undesirable exothermic reaction.
Composite Propellants
435
Fig. 10.9. Enthalpy of formation for major oxidizers as a function of the molecular
weight.
• The availability of different particle sizes in order to obtain high solid
loading and required burning rates.
In practice, the number of oxidizers used in composite propellant is rather
small: ammonium perchlorate (AP) covers most of the cases. Next, ammon-
ium nitrate, HMX and nitroguanidine are used the most. The characteristics
of these products are given in Table 9.
2.2. 7. 7. NH 4 CI0 4
By looking at Table 9 one easily understands why the use of this compound
is so prevalent: it is dense, thermally stable (much more so than the chlorates)
and its decomposition produces only gases of which a large proportion is
oxygen.
SNPE uses, for example, six industrial particle sizes that permit the
tailoring of burning rates from a few mm/s to 70 mm/s at 7 MPa with burning
rate modifiers. They are as follows:
436
Alain Davenas
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Composite Propellants
437
Type
Average diameter (microns)
B
400
b
200
D
100
F
10
M3
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Ml
1
The first two varieties are obtained directly by crystallization, the
others by grinding.
2.2. 7.2. KCI0 4
Very dense and oxygen-rich, this oxidizer has the drawback of giving to the
propellant limited energetic characteristics. In addition, it also leads to high
pressure exponents.
2.2. 1.3. NH 4 N0 3
This oxidizer, with very low A H (o and with little oxygen available, leads to
specific impulses that are much lower than those obtained with the perchlor-
ates. Its use is generally limited to gas generator propellants, where low
burning temperatures (below 2000K) and slow burning rates (1-2 mm/s) are
often sought. In addition, it exhibits a change of allotropic form at + 32 °C,
accompanied by variations of volume causing significant variations in the
properties of the propellants, including deterioration. So-called “stabilized”
varieties have been obtained through cocrystallization with various salts
(such as NiO). This has the drawback of introducing condensable in the
propellant [12]. They are, however, more and more used.
2.2. 1.4. (CH 2 N 2 0 2 ) 4 : HMX
HMX is not an oxidizer, but it is the only product in the table with a
positive enthalpy of formation. As a result, it is used as a supplementary
energetic solid in propellants already having a high level of oxygen.
2.2. 1.5. Nitroguanidine
Nitroguanidine is not an oxidizer either; but the relatively high value of
A H {0 make it useful as a supplementary charge, like HMX, although at a
lesser degree (because of its low density and its deficit in oxygen), particularly
as a moderator of the burning rate of ammonium perchlorate propellants.
438
2.2.2. Fuels
Alain Davenas
The diagram in Fig, 10 permits classification of fuels based on the energy
available for the formation of the fluorides and the oxides. It illustrates:
• The small difference between fluorides and oxides, with an energy higher
than the chlorides;
• The following decreasing order of energetic interest of the fuels, Be >
Li > B > A1 > H and C.
However:
• Beryllium is difficult to use, except for very specific applications, because
of the toxicity of its combustion products.
• Lithium is not dense enough.
• With boron, B 2 0 3 is not obtainable. In reality, sub-oxides are formed due
to the thermodynamic conditions in the combustion chamber. Accord-
ingly, this fuel loses its theoretical energetic advantage, except under
specific environments very rich in oxygen, in the combustion chamber of
ramjets and ramrockets (Chapter 12).
Magnesium is an interesting fuel, although much less dense (1.7) than
aluminum (2.7).
Aluminum is virtually the universal fuel for composite propellants. It is
available in spherical powders, with small diameters (a few microns to a few
tens of microns), and it is well suited for high solid loading. The fine layer of
aluminum oxide, which inactivates the grains in humidity, makes it easy to
handle.
Carbon and hydrogen, which are always present in a propellant because
Fig. 10.10. Energies available through formation of exhaust products.
Composite Propellants
439
they are essential ingredients of the binder, play a major role in the
exothermicity of the combustion, and have a significant advantage over
aluminum by producing gaseous combustion products.
Other fuels such as heavy metals have been tried, including Ti, Zr and Pb.
None of them is being used, except for zirconium, whose cost remains very
high. Its very high density (6.5) and its good combustibility may lend it a
certain interest for applications where the amount of space available for the
propellant is limited (integral booster for instance).
3. Manufacturing and Quality Control Methods
A complete manufacturing cycle of composite propellants could be repre-
sented by the following diagram:
Preparation of the molds
or of the cases
Mixing Operations
Molding 4 —
1
Curing
I
Finishing
1
Control
Any of these operations is delicate, and conditions the quality of the
propellant grains (microscopic and macroscopic homogeneity, effect on the
operational properties). The preparation of the molds and cases is described
in Chapter 13.
3.1. MIXING OPERATIONS
The mixing operation consists of the kneading of a solid phase (primarily
oxidizer and fuel) and a liquid (the ingredients of the binder). It is designed to
produce an homogeneous slurry that can be molded, with a good level of
reproducibility of the characteristics of the propellant.
Because of the high investment costs of a mixing facility, all mixing
operations that are non-pyrotechnic, and can be done outside of the mixing
facility, are done with conventional mixers.
The more important preliminary mixing operations are shown in Fig. 11.
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Fig. 10.11. Premixing operations.
3. 1 . 1 . Preparation of the binder (Premix)
A typical operation will now be described.
The premixing is done in a container equipped with a mixer. After they
have been weighed, the ingredients are put in the container, as follows: the
polymer, the plasticizer and the bonding agent. The mixture is heated to
60°C.
The aluminum is poured into the container with the binder, while
continuously agitating to ensure a good mixing (this is the case at SNPE;
other companies can incorporate aluminum in the propellant mixer).
The kneading is the most important operation in the manufacture of the
propellant. It must last long enough to create a homogeneous slurry, suitable
for casting. It is also an expensive operation, because of the energy and
manpower requirements, and its duration should be as short as possible
without affecting the quality.
In the past, the first mixers used for the manufacture of propellants were
horizontal mixers. The drum was made of stainless steel to avoid corrosion
from the perchlorate. Two rotating Z-shaped blades would knead and cut the
slurry. The clearance between the wall of the drum and the edge of the blades
was very small — a few millimeters — to minimize the amount of dead space
where the blades could not reach, and the intense shearing action was
designed to ensure a good level of homogeneity in the slurry.
Some kneading phases require the slurry to be heated; others that it be
cooled. This was achieved through a mixer with a double-wall system, where
a circulating liquid could be either heated or cooled at will.
Humidity is bad for all propellant compositions. All facilities where there
are mixers are air-conditioned, and the mixers themselves are closed with a
tight-fitting lid. This lid is equipped with a vacuum device, used to obtain a
low residual pressure of about 10 mm of mercury. Volatile components,
water, and air trapped in the slurry are easily removed in the course of the
kneading phase.
Composite Propellants 441
Over the past 15 years the horizontal mixers have been gradually replaced
with vertical mixers with two or three blades, and an orbital motion.
The process for the mixing operations on these vertical mixers has
remained virtually unchanged from the horizontal mixers; but flexibility and
production rates have greatly increased, due to the possibility of exchanging
the drums. The time required to load and unload the mixers has been cut
down to a minimum.
The vertical position of the blades completely prevents the bearings and
seals from having any direct contact with the propellant mixture, thus
avoiding contamination of the gearbox: cleaning of the mixer is easier and a
higher level of safety is attained.
The sequence of mixing operations is as follows:
The binder is first freed from any gases, after which the oxidizer is
introduced. This may be done manually, repeating the operation several
times (in the case of a small mixer), or remotely, using a hopper equipped
with a vibrating chute or an Archimedes’ screw, in a dry environment.
This is a very important phase because the order of introduction of the
various oxidizer particle sizes, as well as the timing of the introduction,
determine the viscosity of the slurry.
Both the various parameters of the process, as well as the formulation
(wetting agents, bonding agents, particle size distribution of the oxidizing
solids and the type of aluminum and its particle size), are optimized to obtain
a slurry which is as fluid as possible. Better filling of the mixer is possible, and
the mixing times are shorter.
In Fig. 12 is an example of the evolution of the torque of the mixer for two
Fig. 10.12. Torque build-up during mixing.
442 Alain Davenas
propellant compositions both containing 90% solids, but differing by the
bonding agent used.
The introduction of the oxidizer is the most critical phase in terms of safety.
The propellant is not a homogeneous slurry yet, and ammonium perchlorate
in contact with fuel is sensitive to mechanical stimuli. If this inhomogeneous
and porous slurry ignites, the combustion to detonation transition pheno-
menon may take place.
This phase is followed by a homogenization designed to improve the
wetting of the solids by the binder and to decrease the viscosity to the point
where casting can be performed under good conditions. Specimens may be
taken during this phase to check on the oxidizer content and on the burning
rate.
The crosslinking agent and the polymerization catalysts are usually
introduced last, a few tens of minutes before the end of the mixing operation.
The propellant slurry is transferred to an isothermic container, when
horizontal mixers are used, to be transported to their casting facilities. In the
case of a vertical mixer, transport is done by moving the entire drum.
3. 1.2. Continuous mixing processes
For a long time, research work has been devoted to processes that could
lead to continuous mixing as a substitute to the batch mixing process. Since
this evolution has an important effect on the whole process of production of
the propellant grains it will be described at the end of this book in the chapter
devoted to the future of solid rocket propulsion.
3.2. CASTING OF THE GRAINS
3.2. 1. Sequence of operations
There are three major phases involved in the molding of composite
propellant grains:
• First, the filling of the structures and the molding of the central port of the
grains, or of the aft face of the grain.
• Second, the polymerization or crosslinking of the propellant. This is the
“curing” phase which takes place in an oven, or directly in the casting pit
if the grain is very large.
• Third, demolding, machining of the central port and faces when neces-
sary, and finishing operations to give the propellant grain its final aspect.
Typically, the process followed is:
To start, the mold, usually the body of the rocket motor with the inside
surface completely coated with the liner, is filled with the propellant slurry,
coming directly from the mixer.
Composite Propellants
443
This is a delicate operation. There is a wide range of propellants and
various types of behaviors can be characterized: some propellants flow well,
some propellants stick to the walls, some are very viscous; there is also a great
variety of products manufactured, from the small propellant grains for
rockets to the grains for space or ballistic missiles. They must, every one of
them, be perfectly molded, and devoid of any casting defects.
The most widely used technique is “vacuum casting”; an alternative
technique is injection under pressure, called die-casting. Both are described
below.
When manufacturing propellant grains that have a central port, conforma-
tion is ensured by casting with a mandrel, either as a monoblock or in several
parts. The mandrel is placed inside the case before the propellant is cured.
This operation is a simple one when the core can be easily put in place and
extracted from one of the end faces of the propellant grain. Furthermore, if
the space between the walls of the structure and the mandrel is large enough
to allow the propellant to flow well, and for a progressive casting to be done,
the mandrel is installed in the case before the casting operation begins. When
this is not the case, the molding of the central port is done after the casting
has taken place: the mandrel, guided from the outside, is driven progressively
into the propellant by applying pressure.
An intermediate solution consists of using a two-part core. The grain is cast
with the first, lower part already in place. The top part is placed on the
bottom part after the casting has been completed.
3.2.2. Rheologic characteristics and casting
processes
The choice of casting process, of the size of the casting devices and the
definition of the casting conditions, depends, in addition to the size and the
shape of the future grain, on the flowing ability of the non-polymerized
propellant slurry.
Data on the behavior of the propellant during vacuum or injection casting
is provided by its rheologic behavior law. It is specific to each formulation,
and ties the shear stress t, a function of the load imposed on the material
(such as pressure, gravity, and others) to the resulting rate of deformation y.
This law is determined by using a rheometer, an instrument with a
revolving cylinder body placed inside a cylindrical container. A rotation
speed Q is imposed, and the value of the resulting torque Jt is recorded.
The law is determined based on the curve Jt as a function of Q, converted
into the shear stress rasa function of the stress rate (t is expressed in Pascals
and y in s" 1 ):! = /(y).
Precise plotting is necessary for low levels of shearing (y < Is -1 ), corre-
sponding to the conditions that are typical during gravity casting.
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Afain Davenas
Fig* 10.13. Typical rheograms, as a function of time after introduction of the
crosslinking agent (hours-minutes).
The viscosity is determined, for a given shear rate, by the ratio r/y. Typical
examples of rheograms are given in Fig. 13.
There are three major types of behavior:
• Compositions exhibiting a Newtonian behavior: their viscosity is con-
stant, therefore independent from the casting conditions.
• Compositions exhibiting a pseudo-plastic behavior: their viscosity dimin-
ishes when the shear stress is increased. This particularity occurs regu-
larly, although it is more or less pronounced.
Such a slurry does not spread well, but is well suited for die-casting.
• Compositions exhibiting an expanding behavior: contrary to pseudo-
plastic compositions, their viscosity increases with the shear rate. This is
fairly rare. Such a propellant would present great difficulties if it had to be
injected.
Knowledge of the behavior law provides information that is useful to select
the casting process for the propellant and the conditions under which it
should take place. It allows the prediction of the flow rate of the slurry in the
existing casting facilities and the calculation of the number of grains that can
be cast within a period of time compatible with the pot life of the propellant.
Composite Propellants
445
3.2.3 . Description of the major grain casting
processes
3.2.3. 1. Vacuum casting process , by gravity
The oldest process is the vacuum casting process, illustrated in Fig. 14.
The mold, which most of the time is a thermally protected case covered
inside with a liner, is placed in an enclosure that can be heated, and its
pressure lowered between 10 mm and 30 mm of mercury. The purpose is to
obtain a complete degassing of the slurry, a necessity for the manufacture of
grain without voids.
According to the size of the object manufactured, the enclosure is shaped
like a “closet” or a “bell” for small to mid-size grains, or a casting pit for large
grains for space launchers or ballistic missiles.
The casting bowl which contains the propellant is placed above the
enclosure. It is linked to the top of the enclosure by a duct, called the casting
pipe. The end of this pipe opens into the casting enclosure, above the case to
be filled. It is equipped with a slit plate.
This slit plate divides the slurry into strips during the casting to ensure
efficient degassing of the propellant.
It also organizes the flow of propellant so that it falls directly and is fairly
well distributed between the mandrel and the case in grains with a central
Safety vent hole
Fig. 10.14. Casting.
446
Alain Davenas
port. Because of the difference of pressure between the casting bowl and the
enclosure, the propellant flows continuously from the drum to the casting
matrix. Coming out of the slit plate, and according to the design of the slit
plate, the flow takes the shape of fillets or ribbons of slurry which pile up
inside the structure and settle under the effect of their own weight.
The selection of the casting flow rate is the result of a trade-off between:
• The need to have a rapid flow to accommodate time-saving industrial
requirements and to avoid a significant increase of the viscosity due to the
progress of curing.
• The need for a fairly slow flow to permit sufficient degassing of the slurry
after it has gone through the slit plate, and spreading inside the case
necessary for a high quality casting.
The selected flow rates are a function of the geometry of the grains, and vary
from several kilograms per minute for small grains to flow rates of several
hundreds of kilograms per minute for large grains.
The gravity casting process continues to be most widely used today,
because it sufficiently satisfies the needs of propellant casting.
It is a simple process, well suited to the use of large quantities of material.
In contrast to other casting and molding industries (plastics, loaded polymers
and others), large quantities of material are involved for each object.
This process affords all necessary guarantees of safety, considering the
sensitivity of the materials used, and ensures good overall quality.
It is well suited for the low production rates most often used in this
industry.
3. 2. 3.3. Die-casting process
The characteristics described above also point out the limitations of the
process. The design of higher-performance motors, which are highly specia-
lized in terms of their missions and require the lowest possible cost, implies
the manufacture of objects with more complex shapes: for example, bi-
composition grains, long grains, and grains with small diameter and little
space available between the case and the mandrel.
High-performance propellants may also exhibit high viscosity in the
casting phase, which is due to the use, for example, of very fine perchlorates or
high solid loading ratios.
Finally, the manufacture of certain small objects requires high production
rates to allow significant cost reductions.
This led to the study and development of casting processes by injection
under pressure: die-casting. This process involves forcing the slurry to move
by subjecting it to pressure, and using that pressure to fill the molds rather
than simply relying on gravity.
Composite Propellants 447
The various methods used to apply pressure have led to the development of
several specific processes:
(a) Pressure applied using a gas (Fig. 15)
The propellant is placed in a flexible and deformable pouch. This pouch,
located in an air-tight enclosure, is linked to the mold through a suitable
linking system. The enclosure is filled with a gas under pressure which presses
upon the outside surface of the pouch. The propellant is pushed into the
mold.
This process is well suited to the manufacture of small objects with
complex shapes, and produced in small series.
Pneumatic jack p
\ J1L Compressed air
[ Coring
Rrj Compressed air J
Vacuum and sight tube
Spring latches
\
Propellant
Safety seal
Double-acting jack||^^
Mold to be filled
by injection
Openings for injection
Flexible pouch.
Rupture at 50 MPas
Nitrogen
Hydraulic opening
and closing of
the mold
Fig. 10.15. Illustration of injection casting.
(b) Pressure exerted mechanically, using a hydraulic piston
This is the most simple of systems. The propellant is placed in a drum
similar to the casting bowls described above. The drum is linked to the
bottom of the mold by a pipe. Pressure is exerted on the slurry with a
scraping piston placed on top of the propellant.
The propellant, under the pressure of the piston, continuously without any
interruption into the mold, and fills it. The level of propellant increases inside
the mold. This type of casting is known as spring casting.
448
Alain Davenas
One interesting evolution of this classic process has led to the casting
process by “stamping” [14]; it is illustrated in Fig. 16.
In order to minimize the waste of slurry inside the pipes linking the drum
to the mold, and to allow the casting of a large number of cases in one single
operation, the cases are placed directly on the piston, which has been
perforated with a specific number of holes, to allow a direct connection
between the propellant in the drum and the cases. This setup is mounted on
the drum containing the propellant, and is pushed in by applying pressure.
When the pressure is exerted, the propellant goes up and fills the cases. A
valve system closes each case when it is filled. The entire setup, piston and
cases, is located in an oven. Each propellant-filled case is removed from the
piston after cure of the propellant.
This process permits casting of a very large number of case-bonded grains,
in one single operation.
(c) Pressure exerted mechanically, using an Archimedes'
screw
This process is developed from a special type of mixer: the mixer-extruder
(Fig. 17).
The mixing is done in the usual way, in a drum equipped with Z-shaped
blades. This mixer, however, has at the bottom an Archimedes’ screw used to
extrude the product through a threaded-cylinder type of opening at a
pressure calculated as a function of the rate of rotation and the rheologic
characteristics of the propellant.
Composite Propellants
449
By linking this opening to the bottom of a case or set of cases, the
propellant can be transferred directed from the drum, where it is kneaded
under vacuum into the cases without being exposed to atmosphere.
Many grains require central port profiles that cannot be obtained simply
by casting. Several techniques are available:
• Machining of the deep axisymmetric slots using an especially designed
tool at speeds tailored to the material [15].
• Using segmented mandrels. This technique, although simple in principle,
requires in practice the use of complex machinery with safety handling
problems that need to be resolved: the mandrel must be kept tight, and
there is the issue of safety when removing the pieces of the mandrel.
Consequently, this method is used only when central port configurations
cannot be obtained through casting with removable monoblock core, or
through machining, as with fynocyl grains, for instance. It is also used for
maximum loading ratio grains which must be manufactured by integral
molding, and for which mechanical finishing operations are not per-
missible.
• Using mandrels that are destructible after curing of the propellant, or at
the time of ignition.
The technological and implementation difficulties involved with multiple-
segment mandrels led to research on simpler concepts, and resulted in the
creation of mandrels made of a material, either braided or in strips, wrapped
in a very specific pattern, compressed and coated with an elastomer or a
polyurethane foam. The easiest cases can be handled with a simple foam with
sufficient rigidity and capable of disintegrating at ignition. With this process,
grain configurations can be obtained that would be completely impossible
450
Alain Davenas
using either the machining process or the mechanical removable mandrel.
This process places no limitations on configurations or geometry.
This description of casting principles may convey the impression that these
technologies are simple. In reality, however, numerous issues have to be
checked and eventually resolved to arrive at a qualified and reliable process,
such as: air- tightness of the toolings; safety in regard to sensitivity to friction
and static electricity of the propellant; compatibility between the inert
materials involved and the propellant; and temperature and internal pressure
stresses during cure. Without any doubt, most of the knowledge necessary for
the manufacture of performing, reliable propellant grains, at an attractive
production cost, is applied to this area rather than to the more spectacular
area of propellant tailoring.
3.3. TEMPERATURE CURING AND FINISHING
Temperature curing is designed to accelerate the crosslinking reactions, i.e.
harden the propellant rapidly. This is done by raising the propellant to a
moderate temperature while in the casting pit or in an oven.
Changes in the curing process made to improve the properties of the
propellant grains are further described below.
3.3.1. Curing under pressure
The 1960s saw the emergence of composite cases, which offer the significant
advantage of being lighter than metallic cases but are also more able to
deform when subjected to internal pressure.
Benefit can be derived from the latter characteristics to minimize residual
stresses/strains occurring in the grain caused by thermal shrinkage when
cooling after cure.
The leading concept of this process consists in subjecting the case loaded
with the propellant to a pressure during cure such that, when depressurized,
the movement of the case will follow, almost perfectly, the predicted
contraction of the propellant grain when cooling [16].
By decreasing residual stresses/strains, the mechanical safety coefficient is
improved. Curing under pressure is also reflected by an increase of the
volumetric loading ratio of the case and higher quality of the propellant.
3. 3. 2. Integral molding
For productivity reasons, or for production of specific grain configura-
tions, as well as for safety reasons (avoiding trimming the grain by machining
it with a cutting instrument), the integral casting or molding technology is
increasingly being used.
Composite Propellants
451
With this process, which can be coupled with curing under pressure if need
be, the propellant grain is obtained directly by casting, as shown in Fig. 18.
The implementation of the integral molding process involves the following
considerations:
• An absolute thermal control of the casting-curing cycle — which must be
isothermal — only very small temperature changes (positive) are permis-
sible, and after the final tool has been applied to ensure complete
confinement, negative temperature changes are forbidden, for risk of
creating cavities.
• The viscosity build-up of the slurry and the development of mechanical
properties during cure, as well as the thermal characteristics of the grain,
determine the curing cycle.
3.4. INFLUENCE OF THE MANUFACTURING PROCESSES OF
PROPELLANT GRAINS ON THEIR FUTURE COMBUSTION
CHARACTERISTICS AND MECHANICAL AND STRUCTURAL
INTEGRITY
3.4. 1. Anisotropy of the combustion
characteristics
Analysis of the pressure and thrust- versus-time curves at firing of the grain
demonstrates that the manufacturing processes influence the burning rate of
the propellant.
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For example, pressure curves recorded during the firing of MIMOSA
grains of composite propellant exhibited differences when the propellant was
cast with the mandrel already placed in the mold or if the mandrel was
introduced after casting.
The pressure- time curve shown in Fig. 19 for the first process shows a
characteristic hump occurring approximately halfway through the web
burned, while the pressure curve for the second process is flat.
The most important known findings are:
• Halfway through, calculations demonstrate that the burning rate of
grains cast with the mandrel in place is always higher by 3-7%.
• The size of the pressure hump is not a function of the burning rate of the
propellant.
Other experiments performed on BATES grains confirm these findings.
Because experiments where grains of this type manufactured using both
processes were extinguished, revealing that the burning surface halfway
through the burned web is very similar to the theoretical surface, the pressure
hump effect must be attributed to a burning rate variation as a function of
web to be burned.
In the United States, AFRPL fired 2500 motors with 7-900 kg of propel-
lants manufactured with 250 formulations for the BATES program. These
firings served to reveal the hump effect [17].
Several explanations have been suggested. At the time of casting, binder-
rich zones are created, in strata, at contact with the walls of the mandrel and
of the case. The binder-rich zones burn slower, which would explain why the
burning rate is a function of the web burned [18]; on the other hand, these
strata are destroyed when the mandrel is inserted.
Fig. 10.19. Pressure curves for the same propellant.
Composite Propellants
453
3.4.2 . Anisotropy of the mechanical
characteristics
Systematic measurements made on propellant specimens removed from
propellant grains tend to demonstrate that these orientation effects, tied to
the casting process, may also have an impact on the mechanical characteris-
tics and, consequently, on the effective safety factor of the propellant grains.
The more pronounced the orientation of the successive layers of propellant
from the casting operation of the slurry into the case, resulting in significant
shearing stresses in the slurry, the greater these effects will be. The viscosity of
the propellant, in particular, plays an important role.
• On large case-bonded grains, manufactured with the classic gravity
casting process through the base of the aft end of the rocket motor,
dissections have shown that the propellant is homogeneous inside the
grain but that the structural integrity deteriorates in the “raised collar”
usually added to allow casting slightly more slurry than necessary to fill
the case of the rocket motor exactly. But this area, considering the local
geometrical narrowing, and because it is subjected to the effects of the
volume variations of virtually the entire propellant mass during tempera-
ture changes, is the most mechanically stressed and strained area at a time
when the propellant is already partially crosslinked. In some sense the
propellant is “damaged”. Variations of 40% have been recorded between
the values of the modulus and the elongation capability of this area and
the rest of the propellant grain.
• Die-casting processes involving a high degree of oriented injection
coupled with high-level viscosity slurries may lead to variations in the
elasticity modulus, ranging from 30% to 40% between the direction of the
casting and the perpendicular direction.
This influence resulting from the casting process of the slurry and the
geometry of the mold may very well have a considerable impact on the
comparisons of characteristics between manufactured grains and grain
specimens designed for quality control, cast from the same slurry.
Constraints resulting from the manufacturing process require that the
specimen designed to control the structural integrity of the grains be an
object tailored to industrial production, easily machined, and with the
smallest possible size.
Systematic analyses have led to the following conclusions: the mechan-
ical characteristics of the control specimen (parallelepiped obtained
through simple casting by gravity) have been found to be representative
of the grain in a great number of propellant grains.
On the contrary, in a specific finocyl grain, the mechanical characteris-
tics of the specimen have been shown to be inconsistent with those of the
propellant grain. Elastic elongations systematically lower in the propel-
lant grain than in the specimen have been observed. A general analysis of
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Alain Davenas
all test data enabled us to discover that this phenomenon was specific to a
particular kind of composite propellant. Further research succeeded in
defining a more closely representative although simple specimen, ob-
tained by casting with a star-shaped mandrel.
A number of assumptions or observations were made in the course of
analyzing this phenomenon:
— The propellant grain and the specimen must have identical thermal
histories. The case of the grain and the core may play a thermal role and
influence the final level of the mechanical characteristics.
— The size of the specimen must be sufficiently large to be representative of
the propellant grain.
— The liners, and thermal insulations may have some effect (such as
migration, for example).
— In the case of significant shearing of the slurry (die-cast or gravity-cast
grain), the phenomenon may be intensified.
3.5. QUALITY CONTROL
The mission of the quality control services is to ensure the quality of the
product, particularly by controlling the following areas: raw materials,
manufacturing operations, finished product.
3.5.7. Overview
Quality control operations on finished products can be divided in two
major categories:
Destructive tests performed on specimens made with identical propellant:
measurement of ballistic and mechanical properties using methods described
in Chapters 4 and 6, and comparison with the specifications established for
the propellant grain.
Non-destructive tests performed on the propellant grains. The non-
destructive quality control tests, although not specific to composite propel-
lants, are described below.
3.5.2. Non-destructive testing or inspection
In opposition to destructive tests that may include testing until failure of
the specimen, non-destructive tests are designed to ensure the quality and
integrity of the material or of their complex assemblies by “inspecting” them
without altering them. These tests commonly fall into three categories:
• Inspection of the mass to identify cracks, cavities or heterogeneities.
• Examination of the bonds to identify debondings, cracks or inclusions.
• Control of the geometry to verify the dimensions.
Composite Propellants
455
With case-bonded grains, it is very important to inspect the most critical
bonding zones which are located, usually at the aft or head ends.
Simple methods, such as visual or dimensional controls, are widely used,
either to observe any surface anomalies, or to check the functional dimen-
sions of the finished object.
Generally, these methods do not call for sophisticated principles. But they
may very well use very intricate methods, such as endoscopy, surface control
devices, television, stereoscopy, laser proximetry, and others.
These methods are useless for the control of the interfaces or the mass of
the propellant grain. It is therefore necessary to have recourse to advanced
technologies that allow us to traverse the material regardless of the nature of
the material encountered.
The most widely used of these techniques are based essentially on the
analysis or the detection of a wave or a radiation after its absorption,
reflection, or emission. The oldest and most prevalent of these techniques call
for ultrasound and X-rays. The most recent ones apply newly discovered
principles, and make use of powerful automatic computer methods that
facilitate the analysis of the information.
The implementation of these techniques usually requires large infrastruc-
tures and costly investments. The selection must therefore be very carefully
made to ensure that the testing facilities will allow performance of quality
control easily, at the best possible price.
The major difficulty encountered comes from the fact that in every case,
there are superimposed interfaces, sometimes located behind a zone normally
not bonded.
This means that one area can hide another and make the methods suitable
for the analysis of the first interface completely useless on the other. The
methods used fall into two categories:
• So-called “global” methods, which generally provide qualitative informa-
tion, over a large area, at one time.
• “Spot” methods, which provide qualitative and quantitative information
over a limited area.
It is desirable for one technique to be capable of providing these two types of
investigations.
3.5.2. 1 . Inner control
The oldest and still yet most widely used methods are based on X-rays and
ultrasonic waves.
(a) X-ray testing (Fig. 20)
This technique allows us to assess the inner homogeneity of the propellant
grain (lack of cracks, bubbles, porosities, foreign matter, for example), the
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Alain Davenas
quality of the bonds between the various elements of the propellant grain
(liner-case or thermal insulation, liner-propellant, propellant-propellant),
and also to determine the thickness of the various components. This test is
based on the variations in the absorption of X-rays by the elements
constituting the grain, which is translated by contrast differences on the
various materials used to receive the radiant image. On film, negative film
usually, cavities and debonding, which have a low absorption, will show as
dark areas; metallic foreign matter, more absorbing, is paler.
X-rays are produced by bombarding fast electrons on a heavy metal target.
The resulting energies may range from 50 keV to a few tens of MeV.
An energy of approximately 2 MeV is produced with a Van de Graaf
electrostatic generator, while a greater energy will be produced with an
electromagnetic linear accelerator.
Analysis of the radiating image, usually captured on photographic film, is a
delicate operation, which requires highly qualified personnel regardless of the
imaging method used: naked eye or microdensitometer.
This is equally true for the radiologist, who must have knowledge of a
collection of parameters which greatly influence the quality, and therefore the
analysis, of the final image. These parameters include:
• intensity of the X-ray;
• type of film used;
• distance of the source to the grain;
• positioning of the film in relation to the grain;
• number of angles of exposure;
• exposure time.
The determination of these parameters is often the result of a trade-off: for
instance, an increase of the intensity of the X-ray results in a shorter exposure
Composite Propellants
457
time, although it increases the graininess of the image on the film. Similarly,
increasing the distance to the grain results in a trade-off between a longer
exposure time and the depth of field.
The optical density obtained on the film varies significantly according to
the area under observation. An average density is necessary to correctly
reveal defects, often requiring the use of films with different speeds. For
instance, the image of the inhibitor-propellant bonds is done with a slow film,
while the central areas will be done with a fast film.
The precision of the measurement of thickness and of the size of the defects
is affected by:
• out-of-focus areas, dependent on the focal length of the radiographic
camera;
• graininess of the film;
• intensity of the radiation, which affects the contrast.
X-ray radiography, followed by analysis of the image on the film, is a slow
and expensive technique for extensive testing; but is a highly precise method
for the observation of the inhibitor-propellant bondings and is widely used
for large propellant grain.
(b) Ultrasonic testing
This technique is based on the observation of the variations experienced by
an ultrasonic wave traversing an object. It is therefore possible to detect the
transmission or the reflection of an ultrasonic wave or to analyze the nature
of the signal (amplitude, frequency, phase).
This type of control is rarely used for mass exploration because propellant
is highly absorbing. It is not very useful in determining the size of a defect.
Still, it is frequently used to check the propellant-inhibitor bonding, though
limited to the first interface only. It may present some interest for the
assessment of the boundaries of bonded areas, and is therefore used as a
method to analyze small areas, using portable equipment.
Other techniques, similar to the one just described, may also be used
sometimes:
• y absorption: this is of limited use because of the pyrotechnic threat tied
to radioactive sources;
• neutrons: cannot be used for high thicknesses hydrocarbon materials;
• acoustic emission: difficult because of the low emissive power of propel-
lants;
• infrared thermography: this is not suitable for superimposed bondings
such as are found in propellants;
• optical holographic interferometry.
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Alain Davenas
New techniques are currently being developed with the help of better-
performing and more modern techniques for the recording and analyses of
the image.
(c) New investigation methods
The purpose of these new techniques is to:
• remedy the shortcomings of classic radiography by, for instance, aiming
for rapidly available information, in real time;
• provide a reception level tailored to the requirements;
• respond to the need for spatial observation;
• answer the necessity of recording the information obtained;
• find a high level of cost-effectiveness.
They include:
Televised radioscopy. This technique, which is increasingly used [19] and is
perfectly suited for industrial production, provides the ability for continuous
and dynamic observation (Fig. 21). It combines the use of television, video-
taping and computers. Total observation in real time of a moving object is
TV
TV
TV
— \
1
-
L J
i
No detection
Fig. 10.21. Televised radioscopy: dynamic observation.
Composite Propellants 459
possible from a completely automatic observation post. This observation
post is divided into three sectors:
• information gathering sector;
• analysis sector;
• memory sector.
Through its new design, this technique offers many advantages and contri-
butes to significant savings in testing operations.
Observation with this new technique of, for example, 64 mm diameter
propellant grains, allows us to guarantee the detection of 0.8 by 8 mm
cavities, and of foreign objects with an average diameter above 0.5 mm.
Tomodensitometry. In the medical field, this technology is known as “scan-
ning.” It is the result of a logical evolution of tomography (Fig. 22), itself
derived from radiography. It permits, using a computer, the reconstruction of
images of successive slices of the object, providing a record on film of
information that is not accessible with the classic X-ray method, in particular,
the observation of the inner configuration of a specimen. Through a
reconstruction of a succession of sections it reproduces the three-dimensional
aspect of all areas of the object examined. As with televised radioscopy, the
completely automatic control is an important advantage, permitting us to
acquire, analyze and decide in real time, at a minimum cost (Fig. 23).
This imaging method, used until recently mainly for small objects, is now
being applied to stages of ballistic missiles.
Fig. 10.22. Diagram of the tomography inspection.
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Alain Davenas
Control commands
Data flux
Fig. 10.23. Organization of a tomodensitometry set up.
Compton Scattering . This technique allows the reproduction of images by
computers resulting from the observation of the Compton effect, the scatter-
ing of an X-ray or gamma-ray upon impact with the object examined. One of
the advantages consists of having the source and the detector on the same
side of the object (Fig. 24).
When only the periphery of a very thick object is being checked, this
technique permits the use of less powerful X-ray generators than would be
necessary with the tomodensitometry X-scanning.
Composite Propellants
461
X-Ray
photons source
Compton scattering technique for the detection
and location of density anomalies in the material
4. Properties of Composite Propellants
4.1. ENERGETIC AND COMBUSTION CHARACTERISTICS
(STANDARD DELIVERED PRACTICAL SPECIFIC IMPULSE
IS USED)
4.1.1 . I so I it es (polyurethane-polyether binder,
ammonium perchlorate)
These non-metallized propellants are used essentially for gas generators, or
as “sustainer” compositions for missiles where a low signature (absence of
solid particles) is required.
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Alain Davenas
The specific impulse, like the density, is low: some compositions where a
portion of perchlorate has been replaced with nitroguanidine to adjust the
burning rate at approximately 1-3 mm/s at 7 MPa do not exceed 180-190 s.
4. 1.2 . Butalites (polybutadiene binder ,
ammonium perchlorate )
The burning rate range of these “reduced smoke propellants” is much
wider. They are used for the same purposes, and the tendency is to use them
instead of Isolites. The reduced smoke propellants with the highest specific
impulse attain I s ranging from 235 to 239 s, with burning rates at 7 MPa
which may exceed 60 mm/s if very fine ammonium perchlorate and a high
percentage of ferrocene catalysts are used.
At lower burning rates, on the other hand, the impulses are comparable to
those of non-metallized polyurethane propellants, because the ammonium
perchlorate has to be replaced, in part, by a cooling charge.
4.1.3. Aluminized composite polyurethane
propellants or Isolanes ( polyurethane , ammonium
perchlorate , aluminum)
The standard specific impulse rarely exceeds 240 s, and they are currently
replaced by polybutadiene propellants.
4. 1.4. Aluminized composite polybutadiene
propellants or Butalanes (poly butadiene,
ammonium perchlorate , aluminum)
The conventional aluminized composite propellants with the highest
specific impulse, they are currently manufactured in very large quantities.
They contribute an increase of 5 s over the best polyuretanes, with a density
capable of reaching 1.86. They are used in the most powerful version of
ballistic missiles, as well as in tactical missiles where the range of the burning
rate (more than 60 mm/s at 7 MPa) and excellent mechanical properties are
very valuable qualities.
4. 1.5. Composites with HMX (Butalanes X)
These propellants, with some HMX added, offer a gain of 3-4 s in specific
impulse over the best Butalanes, including, however, a small loss of density.
Composite Propellants
463
4.1.6. Solid post-boost system propellants:
Butamites (polybutadiene binder, nitramine), and
nitramine-based propellants
These propellants, which contain a hydrocarbon binder and a nitramine,
are not used in main rocket motors because of their limitations in terms of
specific impulse and burning rate. However, their kinetic characteristics, their
“cleanliness” and the non-corrosive nature of their gases, and their specific
impulse superior to that of AP propellants make them a better choice when
severe temperature limitations (2000-2500 K) are placed on the combustion
gases in gas generators, or for warhead dispersion systems of ballistic
missiles [20]. An illustration is provided in Fig. 25.
The same types of binders are used as in typical propellants: polyesters,
polybutadienes, and the nitramines are usually HMX or RDX.
Q-
E
o
<1)
Q-
</>
O
<D
}"Oxidizer": HMX
] Oxidizer: AP
Flame temperature (K)
Fig. 10.25. Effect of substitution of AP by HMX for two types of propellants.
Their combustion is rather peculiar: low burning rates, a few millimeters
per second; at low pressure, this burning rate increases with the solid loading
ratio and decreases with the particle size of the nitramine. The pressure
exponents, ranging between 0.5 and 0.7 at low pressure, tend toward 1 above
150 bars, and the burning rate becomes the same as that of pure nitramine
[21,22]. This high exponent makes them particularly suitable for the modula-
tion of the flow rate by varying the pressure.
4. 1. 7. Gas generator propellants: Butanites and
Ammonium nitrate propellants
Also reserved for use with gas generators, these are the “coldest” of the
industrially used propellants ( T c < HOOK). Their burning rates are a few
millimeters per second and their specific impulse is low [23,24].
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Alain Davenas
4.2. MECHANICAL CHARACTERISTICS
These are discussed in Chapter 6; consequently, this section describes only
certain aspects relating to the chemical composition: capability curves and
the kinetic of the development of mechanical properties.
4.2.1. Capability curve
By plotting on a diagram (Fig. 26) the values of the maximum stress S m
versus the maximum strain for various values of the crosslinking or cure
ratio — ratio of the reactive functions of the crosslinking agent and the
polymer — we see that the corresponding point follows a curve characteristic
of the given composition, called the capability curve. For small values of the
crosslinking ratio the mechanical capability is very weak, and S m and e m
decrease simultaneously. For high values of that ratio the elongation
capabilities are very small. For values that are overall close to the stoichio-
metry, the aspect of the curve allows us to determine the best trade-off
between S m and e m , i.e. determining the mechanical properties of the
propellant. Changes resulting from different lots of raw materials — reflected
by slight variations in the reactive function concentrations — must be such
that, to be acceptable, an identical capability curve is obtained.
em (%)
Fig. 10.26. Stress at maximum strain versus maximum strain as a function of the
curing ratio (HTPB, AP, A1 propellant).
4.2.2. Cure kinetics and development of the
mechanical properties
The propellant grains that are being manufactured to be handled without
being damaged must have mechanical properties that are virtually stabilized
at the end of curing. This explains why the kinetics of the crosslinking must be
well determined for each material developed, by measuring the cure state and
the mechanical characteristics during the curing operation at various temper-
atures.
Composite Propellants
465
Fig. 10.27. Example of the build-up of maximum stress as a function of the curing
temperature.
Figure 27 illustrates the evolution of the maximum stress over time for
three cure temperatures. We note that:
• The energy that activates the crosslinking reaction is independent from
the temperature, but slightly dependent on the progress of these reactions.
The value of energy E which allows the best reproduction of the curve at
different temperatures is close to 10 to 15kcal/mole for propellants
formulations based on carboxy or hydroxytelechelic polybutadiene.
• Since generally the cure temperature does not affect the final level of
mechanical properties, we may assume that the state of the propellant
mechanical properties after complete crosslinking is not dependent, at
least within the useful range (40-60°C), on the cure cycle that is being
used.
• A simple model can be used to predict the effect of a cure cycle. The
development of the mechanical properties — maximum stress, for exam-
ple — versus time is expressed by formula of the type: SJS m stabilized =
f(Q) where g, called “cure quantity,” is related to the cure cycle.
• Having determined the relations SJS m stabilized = f(Q ) allows us to
predict the effect of a given cure cycle on the mechanical properties.
4.3. AGING OF COMPOSITE PROPELLANTS
Experience has shown that it is the mechanical properties that can be the
most seriously affected by aging. The thermodynamic and kinetic properties
are rarely modified.
There are numerous factors influencing aging, and their incidence varies
according to the propellant considered.
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466
4.3.1. Temperature
Temperature accelerates the multiple aging reactions, in various ways,
depending on their activation energy.
In practice this means that the determination of the aging characteristics
needs to be done at a temperature as close as possible to the temperature that
will be really encountered, considering the diversity of the possible reactions,
which the temperature does not all accelerate in the same manner.
4.3.2. The environment
Generally, air and humidity are aging factors by initiating oxidation and/
or hydrolysis reactions:
• Oxidations of the double bonds of the binder causing an over-crosslink-
ing, followed by a break of the chains through depolymerization.
# Hydrolysis of certain sensitive functions such as the esters bonds, and also
the action of the water on the binder-oxidizer bond. Beyond a certain
threshold of relative humidity (70-80%), AP absorbs the water, resulting
in the destruction of the binder-oxidizer adhesion, eventually surface
dissolution, and the acceleration of the oxidizing attack through the
formation of perchloric acid.
4. 3. 3. Mechanical stresses
When the mechanical stresses exceed a certain threshold they may result in
a degradation of the material by causing, for example, binder-solid separa-
tions.
An accumulation of the degradations (fatigue) may make the propellant
useless, as is clearly demonstrated by the previously mentioned case of
unstabilized ammonium nitrate propellant (Fig. 28),
Fig. 10.28. Evolution of the properties of an AN-HTPB propellant during thermal
cycles.
Composite Propellants
467
4.3.4. Contact with other organic materials
The propellant is bonded to a liner or a combustion inhibitor. Some of the
elements which are not tied chemically may migrate from the propellant to
the rubber; others may migrate in the other direction and significantly modify
the composition at the interface with consequences which will naturally not
only affect the mechanical properties and the characteristics of the bonding,
but also the burning rate, through the migration of catalysts or plasticizers.
This issue takes on a great importance for end-burning grains where the
burning rate may be greatly disturbed alongside the inhibitor, and cause a
modification in the combustion parameters.
4.4 SAFETY CHARACTERISTICS AND PYROTECHNIC
BEHAVIOR
The composite propellant types Isolite, Isolane, Butalite, and Butalane
generally exhibit high critical detonation diameters, over 1 m, and a low
sensitivity. The introduction of oxidizers likely to detonate such as RDX and
HMX will of course decrease the critical diameter, but composite propellants
may generally be considered not to be very sensitive, thus fulfilling rather well
the specifications for low vulnerability or lower risk. The major mode of
decomposition from stimuli such as friction, shock, impact, or fire, is
combustion. Ammonium perchlorate composite propellants may, however,
exhibit a violent reaction (thermal explosion) at slow cook-off, i.e. a few
degrees per hour temperature increase.
In terms of the manufacture, an analysis of the history of accidents that
have occurred in the composite propellant industry certainly shows that,
outside of special cases where the cause is foreign to the product itself
(presence of foreign bodies, external stimuli, or equipment malfunction for
example), and until the development of high burning rate propellants and
HTPB binders, the major causes of accidents were linked to the handling of
the wastes, more or less inhomogeneous, of perchlorates and other oxidizers
contaminated with grease or organic matters, or to mixtures (dust, for
example) of solid oxidizers and fuels. This explains why, in the manufacture of
propellants, very rigorous attention must be paid to keeping oxidizers apart
from fuels, to the cleanliness of the facilities, and to the handling of wastes or
objects contaminated with propellants. Explosions, even detonations, have
occurred during the destruction of wastes by burning. Their origin is a
transition of combustion to detonation in this sometimes porous and
inhomogeneous medium.
Experience, coupled with a systematic characterization of the sensitivity of
all products at every stage of the manufacture, has permitted the establish-
ment of concrete measures, reflecting the safety margins of operations carried
out during production, that towards the end of the 1960s have generally
become the standards for this industry. These measures have had to be
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Aiain Davenas
drastically amended, however, with the development in industrial manufac-
ture of two new products: high burning rate propellant with ferrocene
additives and HTPB binders which, by making the propellant a very poor
conductor, have caused ignitions of electrostatic origin.
4.4. 1. High burning rate propellants
High burning rate aluminized composite propellants containing high levels
of ferrocene derivatives have been at the origin of many accidents that have
occurred in the industry during recent years [25]. This does not mean that
they should be rejected because, as we saw, they have unique operational
characteristics. However, their greater sensitivity, associated with more
violent effects, demands that the production, handling and quality control
methods be thoroughly reassessed.
Table 10 lists a certain number of sensitivity characteristics of typical
polybutadiene-AP-Al propellants and of propellants with a ferrocene deriva-
tive. The sensitivity tests were performed in accordance with the codified
standards of SNPE (Chapter 7).
The reactivity of the mixture of ammonium perchlorate with a ferrocene
derivative determines the pyrotechnic behavior of the propellant.
Indeed, mixtures of pure products are sensitive to mechanical stimuli, with
a sensitivity level identical to that of granular explosives or of a pyrotechnic
ignition powder. These characteristics, listed in Table 11, determine the
behavior of the finished product, and require that special precautions be
Table 10 Sensitivity characteristics of aluminized polybutadiene composites ( Butalanes)
with a ferrocene derivative
Stimuli
Mode of decomposition
Thermal Mechanical Detonation
AI a Cook-off Shock b CDD d Combustion
Test (°C) (°C) CSF(N) (m) CGT C (mm) K e (mm/s)
With ferrocene derivative
20-30 mm/s
220 155
50-70
1.75
<1
60
4-3
30-50 mm/s
196
50-70
1.25
<1
60
4-5
50 mm/s
190
30-50
0.50
<1
>6
W ithout ferrocene derivative
7-9 mm/s
320 175
140
2-3
<1
1
12-15 mm/s
265 175
90
1.75
<1
1
a AI = Autoignition temperature, heating at 5°C/mm.
b Shock = 30 kg drop hammer test, no-reaction height.
c CGT = Detonation aptitude index, number of cards (French).
d CDD = Critical detonation diameter.
e V = Burning rate at atmospheric pressure.
Composite Propellants
469
Table 1 1 Sensitivity of mixtures of ammonium perchlorate! ferrocene derivatives com ■
pared with explosives
Test
Pure AP
50/50
72/25
90/10 95/5
HMX
PETN
MIRA*
CSF (Newtons)
(friction Julius Peters)
>360
37
20
22
35
100-200
40
34
CSI (Joules)
(impact Julius Peters)
13
5
3
3
2
4-5
3
6
Autoignition
(5°C/mm)°C
-400
275
260
260
295
256
184
300
* Pyrotechnic ignition composition.
observed for the production. In addition, the ferrocene derivative facilitates
the decomposition of perchlorate. Analyses have shown a decrease of the
order of 150°C in the exothermic decomposition peak of the ammonium
perchlorate decomposition. Consequently:
• the higher the content of ferrocene derivative,
• the higher the content of perchlorate,
• the smaller the particle size of the AP,
the greater the reactivity will be.
4.4. 7.2. Decomposition modes
(a) Detonation
The critical diameter of these propellants is much smaller, in some cases as
small as 60 mm, setting them clearly apart from those other types of
composite propellants, although their response is measured by less than one
card at the card gap test.
(b) Combustion
The thermal effects of these formulations present a major threat during
manufacturing operations. This is due to the fact that the combustion
propagates very rapidly to the surface of the specimen following an accidental
ignition.
The regression rate measured during a strand burner test, at atmospheric
pressure, is greater than 3 mm/s, and increases with the amount of ferrocene
catalyst. A test done on a small star-shaped grain shows that a flame 1 m long
appears in a few tenths of a second. This vigorous ignition capability must be
taken into account in the determination of the protective zones for the
personnel during manufacture, and can require remote operations.
470 Alain Davenas
4.4. 1.3. Sensitivity to mechanical stimuli
(a) Shock
In a 30 kg drop hammer test, a 4 m fall does not lead to a detonation, and
the effects are hardly more violent than the effects obtained with typical
compositions. The non-reaction height, however, is much lower than with
typical propellants, which show no reaction below a drop of 2 m: the results
varied between 0.50 m and 1.75 m.
(b) Friction
These compositions are sensitive to friction, in the conditions created by
the Julius Peters testing device (0.4 mm thick blades). Strong reactions were
observed, and the higher the content of ferrocene derivative, the more
sensitive the compositions are (Fig. 29).
While typical propellants have CSF values greater than 70 N, these
propellants exhibit values ranging between 50 and 70 N, lower values can be
recorded for formulations whose burning rate at 7 MPa is greater than
50 mm/s.
Fig. 10.29. Friction sensitivity.
4.4. 1 .4. Sensitivity to thermal stimuli
(a) Autoignition temperature
The presence of ferrocene accelerator lowers the autoignition temperature
to approximately 200°C, and triggers violent decomposition phenomena in
specimens that are not observed with typical propellants, whose reaction
temperature is close to 300°C.
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471
(b) Cook-off
The thermal stability of compositions accelerated by a ferrocene derivative
is lower than that of typical propellants, and this is more so when the particle
size of AP decreases and the amount of ballistic catalyst increases. Cook-off
tests performed with a specimen 50 mm in diameter and 50 mm in height
have demonstrated a 50°C decrease of critical temperature, which, however,
continues to be higher than 125°C.
4.4. 1.5. Sensitivity to static electricity
These propellants are sensitive to capacitive discharges only above a
certain amount of aluminum (SNPE Test No. 37). Although above that
particular amount, the aluminum quality (shape and size of particles) plays a
fairly significant role in this type of stimuli, mechanical characteristics and
temperature may also be important factors.
4.4. 1.6. Production safety measures
While thermal effects are the acknowledged major threat from these
compositions when polymerized, it is nonetheless necessary, because of the
reactivity of the ferrocene derivative with ammonium perchlorate, to adopt
preventive measures for mixing these components.
Ferrocene derivative, for example, may contain volatile ingredients (pure
ferrocene), which by condensing on the cold parts of the mixer, may lead to
mixtures with AP dust that are particularly sensitive to mechanical stimuli.
In general, these manufacturing operations are done under the highest
safety conditions practiced by the industry.
The sensitivity of the various composite propellant families can be illus-
trated with the diagram of autoignition temperature versus sensitivity to
friction shown in Fig. 30.
4.4.2. Detailed presentation of the problems
related to sensitivity to static electricity
Table 12, where the resistivities at 20°C of various binders are given, shows
that the historical development of these binders was accompanied by an
increase of their insulating nature. It is therefore logical that during the
manufacturing process that necessarily includes handling, friction, and
movement of insulating and conductive materials, we would see an increasing
number of occurrences with an electrostatic origin, such as electrostatic
discharges that not only are an impressive sight, but also may lead to
mechanical rupture of the materials.
The development of these propellants was combined with a development of
472
Alain Davenas
Table 12 Volumetric resistivity at 20° C of the major binders of composite propellants , and of
several materials
Nature
Resistivity (fl m)
PU binder (polyurethane based on polyoxypropylene glycol)
6
x 10 8
CTPB binder
7
x 10 9
HTPB binder
2
x 10 12
PVC inhibitor
10 12
Thermal insulation rubber
10 12
Thermal insulation rubber, treated for conductivity
10 4
the insulation and case materials. Metallic cases, for example, were replaced
by highly insulating composite cases that could only aggravate the problems:
the Faraday cage effect of the case disappeared, and the propellant became
sensitive to outer electric fields.
Traditional tests to determine sensitivity to electrostatic discharge, typi-
cally adapted from tests used for pyrotechnic powders, classified the compo-
site propellants as insensitive but at the same time, accidental ignitions were
happening during their manufacture. Little by little the origin of these
ignitions was traced back to static electricity. It was SNPE researchers who
identified the phenomenon [27,28], created a model reproducing the inci-
dents observed during manufacture, recommended practical measures to
minimize these phenomena and, finally, partially clarified the mechanisms
involved.
Composite Propellants
473
The so-called capacitive discharge test was described in Chapter 7.
For propellants identified as sensitive to capacitive discharges, the analysis
of the phenomena observed, such as the occurrence of the cracking pheno-
menon before the ignition phenomenon, suggests that the reaction mechan-
ism can be broken down into two essential phases:
1st phase Emergence of a cracking phenomenon, related to a critical
potential,
2nd phase Emergence of an ignition phenomenon, related to a specific
critical energy.
All observations tend to demonstrate that the reaction begins inside the
propellant. The existence of a critical potential shows that cracking is caused
by one or several electric phenomena.
Among those electric phenomena that have been identified, discharges
between aluminum particles may be considered as the most likely one:
• Aluminized compositions alone were found to be sensitive.
• The volumetric resistivity of pure aluminum powder shows that for a
given critical potential, the value of resistivity changes from 10 7 to
10 3 ft m. This corresponds to a puncture, for a certain number of particles
of the aluminum oxide layer that covers the pure aluminum.
A factor analysis of the active ingredients of propellants essentially revealed
the influence of:
• ratio, particle size and shape of aluminium particles;
• particle size of ammonium perchlorate;
• resistivity of the binder.
Temperature must also be taken into consideration. Some propellants that
are insensitive may become sensitive when the temperature is lowered. When
the aluminum ratio is constant, the decrease in diameter of the aluminum
particles, i.e. their increase in number, leads to compositions that are more
sensitive to capacitive discharges.
A model based on percolation theories was suggested. A “percolation”
coefficient P was identified, such that:
P =
NJN {
°l/Vl
P > 10 10 ft m for sensitive propellants;
(t l = conductivity of the binder;
V L = unit volume of the binder;
N c = number of conductive particles (aluminum);
N { = number of insulating particles (ammonium perchlorate, HMX).
474
Alain Davenas
With ammonium perchlorate we note that the influence of the particle size
plays a role inverse to that of aluminum.
In addition, the volumetric resistivity measurements of binders have
demonstrated that the polyurethane binder with a polyether prepolymer base
is the least resistive. Both polybutadiene binders, on the contrary, are much
more resistive (HTPB binder resistivity at 20°C: 7 x 10 9 Q m; HTPB binder
resistivity: 2 x 10 12 nm).
This classification, based on resistivities, also works well for the sensitivity
scale of propellants. For instance, polyurethanes are not sensitive at 20°C,
and among the polybutadiene HTPBs are the most sensitive.
Bibliography
1. Flory, P. J., Principles of Polymer Chemistry. Cornell University Press, Ithaca, 1953.
2. Abadie, J. M. et a/., Etude des proprietes de polycondensats a base de polybutadiene
hydroxytelechelique. European Polymer Journal , 23, 223-228, 1987.
3. Atlantic Richfield Company, USA., Procede de preparation de polymeres de diene a
terminaison hydroxyle. Brevet fran^ais, 73.23, 114, 25-6-73.
4. Raynal, S. and Doriath, G., New functional prepolymers for high burning rate solid
propellants. AIAA 86-1594, AIAA/ASAE/ASME 22nd Propulsion Conference, 1986.
5. Le Roy, M., Agents d’adhesion liant-charge dans les propergols composites. Colloque du
Groupe Francais des Polymeres, Toulouse, 1978.
6. Farris, R. J., The influence of vacuole formation on the response and failure of filled
elastomers. Transactions of the Society of Rheology , 12 , 2, 315-334, 1963.
7. Finck, B. et al , Agents d’adhesion liant-charge et composition propulsive contenant cet
agent d’adhesion. Brevet francais, 85.13. 871, 19-9-85.
8. Oberth, A. E. and Bruenner, R. S., Bonding agents for polyurethane. United States Patent,
4 000 023, 28-12-76.
9. Graham, W. H. et al ., Control of cure rate of polyurethane resin based propellants. United
States Patent, 4 110 135, 29-8-78.
10. Cullis, C. F. and Laver, H. S., The thermal degradation and oxidation of polybutadiene.
European Polymer Journal , 14 , 571-573, 1978.
1 1. Farris, R. J., Prediction of the viscosity of multimodal suspensions for unimodal viscosity
data. Transactions of the Society of Rheology , 12 , 2, 280-301, 1968.
12. Strecker, R. A. H. and Linde, D., Gas generator propellants for air to air missiles. 53rd
Meeting of the AGARD Propulsion and Energetics Panel, 17-1, 17-11, Oslo, 1979.
13. Tauzia, J. M. et al ., Application de la rheologie au moulage des chargements en propergols
composites. ICT Jahrestagung, 37, Karlsruhe, 1987.
14. Niquet, R. and Quebre, E., Procede de moulage par injection simultanee dans plusieurs
moules et appareillage de moulage correspondant. Brevet francais, 78.02.019, 25-1-78.
15. Broutin, C. et al. , Procede de realisation de blocs de propergol solide et dispositif d’usinage
d’un canal interne dans ces blocs. Brevet francais, 72.06.914, 2-2-72.
16. Quentin, D. and Pontvianne, G., Procede de cuisson des blocs de propergols contenus
dans une enveloppe. Brevet francais, 70-44 752, 11-12-70.
17. Beckman, C. W. and Geisler, R. L., Ballistic anomaly trends in subscale solid rocket
motors. AIAA 82-1092, AIAA/SAE/ASME 18th Propulsion Conference, 1982.
18. Friedlander, M. and Jordan, F. W., Radial variation of burning rate in center perforated
grains. AIAA 84-1442, AIAA/SAE/ASME 20th Propulsion Conference, 1984.
19. Patanchon C. and Mesnage, R., Application de la radioscopie televisee au controle des
moteurs a propergol solide dans la SNPE. ICT Jahrestagung , 137 148, Karlsruhe, 1983.
20. Davenas A., Amelioration des proprietes balistiques et des proprietes mecaniques tout
temps des propergols sans fumee. AGARD Conference 259 Solid Rocket Motors Tech-
nology, 1979.
Composite Propellants
475
21. MacCarty, K. P. et aL, Nitramine propellant combustion. AIAA 79-1132, AIAA/SAE/
ASME 15th Propulsion Conference, 1979.
22. Beckstead, M. W., Modeling calculations for HMX composite propellants. AIAA 80-1167,
AIAA/SAE/ASME 16th Propulsion Conference, 1980.
23. Pogue, G. B. and Pacanowsky, E. J., Some recent developments in solid propellant gas
generator technology. AIAA 79-1327, AIAA/SAE/ASME 15th Propulsion Conference, 1979.
24. Brown, J. L. and Endicott, D. W., The safe manufacturing of catocene containing
propellants. AIAA 87-1705, AIAA/SAE/ASME 23rd Propulsion Conference, 1987.
25. Brunet, J., Detonation critical diameter of modern solid rocket propellants. ADPA Joint
International Symposium on Compatibility, New Orleans, 1988.
26. Kent, R. and Rat, R., Phenomenes d’electricite statique dans la fabrication et la manipula-
tion des propergols solides. ICT Jahrestagung , 423-438, Karlsruhe, 1981.
27. Kent, R. and Rat, R., Static electricity phenomena in the manufacturing of solid propellants.
20th Explosives Safety Seminar of the Department of Defense Explosives Safety Board,
Norfolk, USA, 1982.
CHAPTER 1 1
Advanced Energetic Binder
Propellants
ren£ couturier
1. Background
1.1. DEFINITION OF ADVANCED ENERGETIC BINDER
PROPELLANTS FAMILY
This family includes all propellants composed of a nitrate ester-based
energetic binder in which fillers (oxidizer and, if necessary, metallic fuel) are
incorporated.
Due to their composition, these propellants are intermediate between the
double-base propellant family (nitrocellulose + nitroglycerine or other liquid
nitrate ester) and the composite propellant family (inert binder + charge).
Two very different processes can be used to manufacture them.
• A casting solvent process which uses the manufacturing system for
traditional double-base propellants. The products manufactured by that
process are called composite modified cast double-base propellants
(CMCDB) or elastomeric modified cast double-base if they include an
isocyanate curable elastomer.
• A slurry cast process similar to the process used to produce composite
propellants. These products are referred to as crosslinked double-base
propellants (XLDB) or NEPE propellants (nitrate ester-polyether binder
including high level of fillers) for specific high energy propellants.
1.2. ADVANTAGES OF ADVANCED ENERGETIC BINDER
PROPELLANTS
The necessity to improve performance of conventional propellants for
tactical and strategic missiles was at the origin of the development of this
propellants family.
477
478
Rene Couturier
Chronologically, the CMCDB propellants were manufactured industrially
before the XLDB. Production began in the United States in the 1950s [1,2].
They were a logical continuation of double-base propellants which had
significantly evolved since World War Two. As a matter of fact, the transition
from a single-base casting powder (nitrocellulose) to a double-base powder
(nitrocellulose + nitroglycerine) had allowed a remarkable energetic im-
provement as well as the possibility of tailoring corresponding propellants to
the production of case-bonded grains, due to the improvement of their
mechanical properties.
The inclusion of fillers such as nitramines, ammonium perchlorate, and
aluminum in double-base casting powder was an additional step toward
improvement of the energetic characteristics.
The development of CMCDB propellants, however, ran rapidly into a
number of limitations, particularly when applied to strategic missiles, due to
the manufacturing process involved. These limitations include:
• impossibility of obtaining solids contents that were as high as those of
composite propellants;
• difficulties tied to the production of large case-bonded grains with high
fillers contents and increasingly complex geometries.
Because of the potential advantages of these propellants, the formulations
were redesigned with the purpose of applying new manufacturing processes.
By substituting a nitrocellulosic polymer with synthetic polymers capable of
higher plasticizer amounts as well as a high solid content, a manufacturing
process related to that for composite propellants could be used. With the
advent of XLDB or NEPE propellants a new step had been taken toward the
improvement of the performance of strategic and tactical missiles. This family
of propellants led to the highest energetic levels that are in fact industrially
feasible.
2. Raw Materials
2.1. BACKGROUND
The formulation of a propellant may seem, initially, to be a simple
operation, consisting of mixing additives inside a binder. In reality it is a
complex operation, requiring that the grain designer takes into account all
constraints related to the design of a propellant grain with those of the
manufacturing process; for example:
• meeting the performance requirements (ballistic, mechanical, reliability,
and safety of handling);
Advanced Energetic Binder Propellants
479
• tailoring of the manufacturing process in order to produce good quality
and reproducible propellants, at the lowest cost, and under the best
possible safety conditions.
Empirical knowledge inherited from tradition on the one hand, and the
emergence of better technical tools on the other hand (computer codes, for
example), help determine the best possible solutions to the problems at hand.
Nevertheless, before a goal can be successfully achieved it must be assumed
that, within a well-established manufacturing process, the raw materials, i.e.
the basic ingredients of the propellant, are perfectly known. This implies:
• on the one hand, an in-depth characterization of each of the raw
materials;
• on the other hand, the knowledge of their behavior toward each other, i.e.
the study of their chemical compatibility. Because propellants are consti-
tuted, in large part, of high-energy additives, there naturally exists a
problem of reactivity from ingredients likely to be mixed.
Preliminary chemical compatibility analyses are therefore mandatory for any
new system. Based on the results obtained, the grain designer may or may not
decide to include these additives.
The principle of the chemical compatibility tests typically is based on
measurements of the gaseous emissions of vacuum-tested specimens, versus
time and temperature. Additional tests may be needed to support the verdict
when difficulties are encountered:
• measurement of the enthalpy of decomposition;
• analysis of the decomposition gases;
• use of chemiluminescence for nitrated derivatives testing
2.2. BINDER INGREDIENTS
2.2. 7. Composition of advanced energetic binders
2.2.1. 1. CMCDB binder
The major ingredients of CMCDB binders are:
• Polymer: nitrocellulose;
• Energetic plasticizer: nitroglycerine;
• Desensitizing plasticizers: glycerol triacetate (or triacetin);
• Other inert plasticizers: (if necessary): aliphatic or aromatic esters,
• Stabilizers: centralite, 2-nitrodiphenylamine.
480 Rene Couturier
With the casting solvent process, binder final composition is acquired in
two phases:
First phase: manufacture of a casting powder, with a binder consisting of
the nitrocellulose and possibly a portion of the energetic
plasticizer.
Second phase: the plasticizer complement is included during the operation
where the solvent (nitrate ester + desensitizer) is cast in the
mold loaded with the casting powder.
Depending on the plasticizer amount, it may be necessary to crosslink
the nitrocellulosic network to obtain a good mechanical behavior of the
propellant.
2.2. 7.2. XLDB (or NEPE) binder
The major ingredients of XLDB (or NEPE) binders are:
• Polymers:
• Energetic plasticizers:
• Non-energetic plasticizers:
• Curing agents:
• Chemical stabilizers
nitrocellulose, polyesters,
polyethers, polycaprolactones
and others;
nitroglycerine, butanetriol
trinitrate, triethyleneglycol
dinitrate, and others;
if necessary;
polyisocyanates;
With the slurry process the binders are always highly plasticized, and
therefore crosslinked.
To be of any advantage, the prepolymers must exhibit specific properties:
• They must be liquid during the premix elaboration (prepolymer and
energetic plasticizer).
• They must be capable of handling high plastification ratios without
exhibiting any exudation phenomena after crosslinking.
• These prepolymer-plasticizer premixes must be capable of accepting high
solids contents (approximately 77-80%) and still be cast into complex
shapes. In this regard, the rheology theory of the flow of composite
propellant slurries is applicable.
• After crosslinking, they must keep their elastomeric-type properties so as
to be more capable of withstanding significant elongations over more or
less wide ranges of temperature. This is due to the fact that XLDB
propellants are used mainly in case-bonded grains.
Advanced Energetic Binder Propellants 481
2.2.2 . Polymers
2.2.2. 1. Nitrocellufoses
Nitrocelluloses, discussed in Chapter 9 on double-base propellants, are
primarily characterized by their nitrogen content. The physicochemical and
energetic properties of the polymer derive from that characteristic.
Nitrocelluloses used in rocket propulsion have nitrogen contents ranging
between 11.5% (Q a — 800 cal/g) and 13% (calorimetric value = 1010 cal/g).
In the case of the CMCDB, however, nitrogen contents close to 12.5% are
particularly well suited because the corresponding nitrocellulosic polymers
allow one to meet specific requirements such as:
• inclusion of solid charges (such as oxidizers, fuels);
• introduction of high percentages of plasticizers.
However, nitrocelluloses are semi-crystalline polymers that, unlike polyesters
or polybutadienes, do not have the chain flexibility that facilitates the
incorporation of high contents of charges (70-80%). With CMCDB, whose
basic polymer is nitrocellulose, the solids content compatible with satisfac-
tory mechanical performance is limited to approximately 45%.
2.2.2.2. Non-energetic prepolymers
The prepolymers, which must be liquid at the temperature of the manufac-
turing process, and which are capable, after crosslinking, of both high
plasticizer and high solids contents, are recruited essentially from hydroxy
terminated polyesters and polyethers. Combined with isocyanates, they will
give polyurethane networks.
Some prepolymers that are particularly interesting for XLDB or NEPE
propellant are listed in Table 1.
So far, the most widely used prepolymers are the ethylene or diethylene-
glycol polyadipates and the polyoxyethyleneglycols (PEG). At ambient
temperature, PEG are usually found in a solid state, with a crystalline
structure. They are, however, easily melted at temperature compatible with
the use of energetic plasticizer (50-60°C). When exposed to high levels of
plasticizers the PEG lose their crystalline structure.
The molecular mass of prepolymers ranges from approximately 1500 to
5000. In practice they are adjusted as a function of the propellant specific
characteristics (mechanical properties, especially).
2. 2. 2. 3. Future developments [3]
The performance improvement of XLDB propellants could conceivably be
made by replacing today’s inert polymers with energetic products, keeping, if
Table 1 Some common inert prepolymers
482
Rene Couturier
Advanced Energetic Binder Propellants
483
possible, the same properties. The synthesis process consists generally of
grafting chemical groups with energetic characteristics on the polyester or
poly ether chains, such as: azide, nitro, nitrate, nitramine, fluoronitrate, etc.
2.2.3. Energetic plasticizers
Energetic plasticizers used in mass production are, for the most part,
polyalcohol nitrates (Table 2).
Among these nitrate esters, nitroglycerine is still the most widely used,
because of the high values of its calorimetric value (Q a ) and its density. Its
drawbacks (vapor pressures, which are rather significant over 50°C, sensitivi-
ty to mechanical stimuli, and lower thermal stability over 100°C) are fully
appreciated due to the experience acquired, for several tens of years, with
double-base propellants.
The development of XLDB or NEPE propellants, with high plasticizers
ratios, and whose composition is becoming increasingly different from that of
double-base propellants, requires that a choice be made of the nitrate ester
best suited to the requirements other than the energetic aspect. These criteria
include:
• chemical and thermal stability;
• volatility;
• propensity to migrate;
• manufacturing cost;
• explosive behavior (mechanical stimuli, for example);
• physical and chemical compatibility with the various propellant
additives.
Finally, a major effort is being devoted to the synthesis of new energetic
plasticizers in order to correct some undesirable characteristics of today’s
nitrate esters. For example, molecules carrying nitrated groups (R-N0 2 ),
azides (R-N 3 ) and fluoronitrated groups are being tested.
2. 2. 4. Inert plasticizers
The plasticizers incorporated in the advanced energetic propellants are
similar to those used in the cast double-base propellants (see Chapter 9).
They fulfill, in particular, the same functions: improvement of the manufac-
turing conditions, and/or of some functional properties of the propellant
(ballistic, mechanical, safety).
The most common plasticizers carry ester functions:
Table 2 Characteristics of nitrate esters widely used in rocket propulsion
484
Rene Couturier
5^ 8
5 | -
3^ u
>
c
DC ^3 c
< O o
>5 \* ca
+ 5 + tS
<2, c
(N O
X Z
<->— O Q "
rfl - (N W
I I X z
u— u— u— o
.2
z
Z
>
<D
Q
z
H
x>
X)
hJ
O
o
w
H
H
eg
<
z
H
CQ
H
<u
u
o
o
>*
c
cd
XI
(U
’35
O
O.
s
o
c
o>
o
00
O
Ui
riethylenegl
dinitrate
utanetriol
trinitrate
rimethylolet
trinitrate
U
z
H
CQ
H 1 i
* The values indicated in this table have been measured at SNPE.
Advanced Energetic Binder Propellants
485
Glycerol triacetate (or triacetin):
CH, — CH — CH,
I I I
OCOCH3 OCOCH3 OCOCH,
n-alkyl adipates:
RO— C— (CH 2 ) — C— OR
II II
o o
(R = CH3,C 2 H 5 ,...,C 8 H 17 )
n-alkyl phthalates:
0 — COOR
— COOR
(R = C 2 H 5 , C 4 H 9 ,
c 8 h 17 )
2 . 2 . 5. Curing agents
Crosslinking is necessary:
• For propellants using highly plasticized nitrocellulose, in order to streng-
then the existing three-dimensional polymeric network whose chains,
held by low-energy links (Van der Waals or hydrogen type), are stretched
by an excess of plasticizer.
• When using hydroxy-terminated prepolymers, also in a highly plasticized
environment; these prepolymers are usually liquid during the mixing
(global process).
The curing agents are designed to react with some functions of the polymers
or prepolymers so as to create a three-dimensional network that will ensure
the cohesion of the cured propellant and, as a result, determine its mechanical
properties.
The polyisocyanates are the most used with the energetic binder propel-
lants. Diisocyanate may be enough to ensure the spatial cohesion of
nitrocellulose. With diol prepolymers this cohesion c&n be ensured either
with a system of triol/diisocyanate or with a polyisocyanate having a
functionality greater than 2. Some of the polyisocyanates widely used in the
field of crosslinked propellants are listed in Table 3.
The crosslinking density, which influences the mechanical properties of the
final propellant, is controlled by:
• the NCO/OH ratio, which expresses the relationship between the number
of available isocyanate functions and the number of alcohol functions;
486
Rene Couturier
Table 3 Some common isocyanates
Type
NCO/kg
Diisocyanates
Hexamethylene diisocyanate (HMDI)
11.7
Toluene diisocyanate (TDI)
11.4
Isophorone diisocyanate (IPDI)
8.9
Functionality polyisocyanates > 2
Tri(isocyanato-6 hexyl)-1.3.5 biuret
5.2
• the ratio: (OH of the triol)/(OH of the diol) with diol prepolymers
involving a diisocyanate-triol system;
• the nature and the amount of crosslinking catalyst.
For a given composition, in a well-defined environment (temperature,
agitation speed), the crosslinking kinetics depends on the nature of the
polyisocyanate. It may, however, be regulated by adding catalysts. Very basic
amines such as triethanolamine, frequently used for the manufacture of
polyurethanes, are prohibited with energetic binders because of their great
chemical incompatibility with nitrate esters.
The burning rate modifiers, particularly lead-base, also have a crosslinking
catalyst effect, more or less pronounced according to their nature (Example:
PbO, Pb0 2 ).
2.3. FILLERS
Performance improvement of energetic binder propellant requires the
incorporation of fillers (oxidizers or mixture of oxidizers and fuels).
The maximum of the solids content, compatible with good feasibility and
acceptable mechanical properties, is determined by:
• manufacturing process (casting solvent or slurry cast);
• binder composition (nature of the polymer, plasticizing ratio);
• shape and size of the solid particles. The use of several particles
sizes — whose average diameter ratios range between 5 and 10 — facili-
tates high fillers contents;
• use of bonding agents facilitates higher solid level as well as particles
greater than 10 microns.
2.3.1 . Oxidizers
The most common oxidizers used in the advanced energetic propellants
are:
Advanced Energetic Binder Propellants
487
• Ammonium perchlorate (NH 4 C10 4 )
• Nitramines:
RDX (C 3 H 6 N 6 0 6 )
HMX (C 4 H 8 N 8 0 8 )
Their main characteristics are discussed in Chapter 10.
2.3. 1. 1. Ammonium perchlorate
Incorporated in energetic binders, this oxidizer decreases the self-ignition
temperature. Compatibility tests performed on ammonium perchlorate-
nitrate ester mixtures reveal a special behavior, which is expressed by a
first phase devoid of any noteworthy production of gas, followed by a
sudden emission accompanied by a fairly violent decomposition pheno-
menon.
2.3. 1.2. Nitramines
The nitramines are:
• RDX or cyclomethylenetrinitramine,
• HMX or cyclomethylenetetranitramine
RDX crystallizes in an orthorhombic form. HMX, on the other hand, may
present four crystalline varieties (a, y and S). Only the form thermo-
dynamically stable and the least sensitive to mechanical stimuli, is used
for industrial manufacture. Both varieties a and y may occur, however, based
on the nature of the recrystallization solvent that is used. As for form S , it
is found only beyond 160°C.
As a result it is necessary, during the manufacture of energetic binder
propellants, to prevent any possibility of solubilization of HMX (in the
cleaning solvent of the tools, for example), to avoid being faced with the risk
of later recrystallization in a or y varieties, which are more sensitive.
Nitramines are powerful explosives, sensitive to shock and to friction. They
must therefore be handled with all precautions inherent in high explosives:
avoid the creation of dusts and friction areas; use remote handling during the
most delicate operations.
RDX and HMX have similar thermodynamic characteristics, but because
HMX has a higher density it results in more energetic propellants (if the
volumetric specific impulse is considered).
Finally, it must be noted that the manufacturing costs of HMX are much
higher than that of RDX.
488 Rene Couturier
2.3.1. 3. Ne w oxidizers
The synthesis research is essentially devoted to the development of dense,
high energy molecules [3]. New specifications have been emerging, however:
• reduction of the sensitivity (related to the development of propellant with
lower vulnerability);
• possibility of controlling the burning rates.
2.3.2. Fuels
Aluminum is widely used in advanced energetic binder propellants as a
solid fuel. It is a metal with a high combustion heat, allowing an increase in
the burning temperature of propellants. However, for its combustion, a
sufficient quantity of available oxygen is necessary. As a result, in the case of
high-energy propellants the oxidizer/fuel ratio must be adjusted in order to
optimize the specific impulse.
2.4. VARIOUS ADDITIVES
2.4.1. Chemical stabilizers
Advanced energetic binder propellants, like all other double-base propel-
lants, present a problem of chemical stability, inherent in the slow decomposi-
tion of the nitrate esters.
To delay this self-decomposition phenomenon, additives with a slightly
basic nature are incorporated in the propellants, so as to block the nitrogen
oxides that are released. The most widely used stabilizers have been described
in the chapter on double-base propellants (Chapter 9).
Use of very energetic crosslinked propellants, that sometimes include the
combination of products that are not very chemically compatible (nitro-
glycerine-ammonium perchlorate, for example), requires the develop-
ment of ever more efficient new stabilizing systems. The criteria for
selection are usually based on the following factors:
• the highest possible nitrosation kinetics;
• good solubility of the stabilizer in the propellant;
• good thermal stability of the nitrosated derivatives.
2.4.2. Ballistic modifiers
Energetic binder propellants without ammonium perchlorate can be
characterized, in a first approximation, by a burning law of the type r b = a p n
Advanced Energetic Binder Propellants
489
where n, the pressure exponent, is generally high (n > 0.8). For these
propellants to hold any interest it is necessary to decrease their pressure
exponent and to be able to regulate their burning rate.
Burning rate modifiers incorporated in advanced energetic propellants
usually come from the classic double-base propellants [3].
2. 4 . 3 . Other additives
Specific additives may be included in propellants to take into account the
operating characteristics of the grain or its type of application, e.g. instability
and/or flash suppressor additives.
3. Manufacturing Processes
3.1. MANUFACTURING PRINCIPLES OF ADVANCED
ENERGETIC BINDER PROPELLANTS
The manufacture of these advanced propellants may be done according to
two techniques with very different principles:
• A casting solvent process consisting of two major steps:
— manufacture of a casting powder, made of the nitrocellulosic binder
containing all solid additives, and if necessary, a portion of the
energetic plasticizer;
— manufacture of the propellant by injection of a casting solvent into a
mold loaded with the casting powders defined for the preceding
process; this casting solvent is composed of a nitrate ester and
desensitizer mixture. The cohesion of the whole is obtained by
curing.
• A slurry cast process is related to the manufacturing process of composite
propellants. Its principle is based on the preparation of a slurry, contain-
ing all constituent elements of the propellant, which can be poured into
the mold either by gravity or by injection. The cohesion of the whole is
obtained during curing by the crosslinking of the polymer.
3.2. MANUFACTURING PROCESS OF CMCDB PROPELLANTS
CMCDB propellants are in fact an extension of the cast double-base
propellants. Consequently, their manufacturing process is similar to that
described in Chapter 8. Therefore, some adjustments are necessary by the
presence of fillers, or of necessity of crosslinking.
490 Rene Couturier
3.2 . 1. Influence of solid fillers (e.g. nitramines,
ammonium perchlorate)
In the manufacturing process of casting powders the charges are intro-
duced during the kneading of the dough. The solvents composition must be
optimized to promote the coating of these charges by the nitrocellulosic
binder in order to obtain densities that are as high as possible in the finished
granules.
In addition, the presence of the fillers is likely to modify the surface of the
casting powder (creation of roughness, for example), which has the direct
consequence of altering the packing density.
5.2. 1. 1. Remarks on the screen loading density (SLD) and the
packing density
To evaluate the packing density, measurements of the screen loading
density (defined by the powder weight in a determined volume) are done
on the casting powder. These gravimetric densities depend on several
parameters:
• density of the granules;
• their geometry: size, length/diameter ratio;
• imperfections of their surface, which affects the flow (importance of the
glazing cycle);
• filling method.
According to the theoretical analyses [5] that have been done on casting
powders, the screen loading densities are at their maximum when the L/D
ratios are close to 1 (Fig. 1). Experimentally, it is preferable to use a L/D ratio
Fig. 11.1. Evolution of the packing density of the molds versus the L/D ratio of
casting powders.
Advanced Energetic Binder Propellants
491
close to 1.2 to be in an area of the diagram capable of tolerating some
scattering of the dimensions, without necessarily having a significant in-
fluence on the packing densities.
The presence of solid charges in the casting powders influences noticeably
the values of SLD. Increasing the particle size for a constant filler content or
increasing the filler content for a constant particle size leads systematically to
a decrease of SLD. The aspect of the surface alone is responsible: more or less
granular aspect, which inhibits the sliding of the grains against each other.
Figure 2 shows the evolution of SLD of the casting powders loaded with 60 %
fillers when the particle size changes from 90 /mi to 15 fim. The volumic
packing density of the mold follows the same tendency. As for the role played
by the fillers contents, it is made quite clear in Table 4.
To increase the packing density one may :
• work with the size of the casting powder (Table 5);
• adapt the industrial process for filling the molds; for example, there are
Fig. 11.2. Comparative evolution of screen loading densities (SLD) and of packing
densities versus the particle size distribution (casting powder with 60 % solid charges).
Table 4 Influence of the fillers content on the screen loading density ( SLD) and the packing
density of the molds
Fillers content (%)
45
60
45
60
Particle size (pm) of fillers
90
90
15
15
SLD (g/1)
970
825
1035
1010
Volumetric packing density (%)
66.0
60.5
71.0
68.0
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Table 5 Influence of the size of casting powders on screen loading density ( SLD) and packing
density of the molds
Filler
Content (%)
Particle size (pm)
60
90
Diameter of casting powders (mm)
0.9
1.5
2.0
SLD (g/1)
810
945
985
Volumetric packing density (%)
60.5
67.0
67.5
specially designed hoppers which allow both a regular flow rate of the
granules, and a good distribution of the granules in the molds.
3.2.2. Incidence from crosslinking
The curing agents used to reinforce the highly plasticized nitrocellulosic
networks are usually isocyanates which will react with residual alcohol
groups of the nitrocellulose (combined if necessary to a hydroxy-terminated
prepolymer). The isocyanates, slightly agitated, are introduced in the casting
solvent just before the casting operation.
To ensure optimal crosslinking conditions, the humidity content of the
various constituents must be as low as possible (a few hundred ppm).
Therefore, particular attention must be used when degassing the casting
powders and the casting solvent, which is done before the casting.
During the curing phase the casting solvent, which diffuses in the granules,
serves also as a vector for the crosslinking agents, which usually have a high
steric arrangement. At that time a competition takes place between the
diffusion and the crosslinking kinetics, which requires the identification of a
curing cycle designed to provide strengthening, as uniform as possible, of the
nitrocellulosic network. Should the temperature conditions not be correctly
adjusted, a superficial crosslinking of the casting grains may occur, hindering
any further diffusion of the casting solvents.
3.3. MANUFACTURING PROCESS OF HIGH-ENERGY
PROPELLANTS (XLDB-NEPE)
3.3.1. Background
XLDB propellants consist of an energetic binder with a high level of
plasticization, in which solid charges are incorporated (oxidizers, fuel,
various additives).
The following are the main reasons for the development of this family of
propellants:
Advanced Energetic Binder Propellants
493
• possibility of obtaining high total solid contents (up to 75% approxi-
mately), allowing an improvement of both the specific impulse and the
density;
• manufacture of propellant grains similar to composite propellants,
making it possible to benefit from all technologies developed so far.
3.3.2. Manufacturing flow sheet
Although the manufacture of XLDB propellants is related to that of
composite propellants, the processes and equipment had to be adapted to
take into account the presence of liquid nitrate esters. This is due to the fact
that the energetic plasticizers involved (nitroglycerine or others) are mixtures
that are sensitive to mechanical stimuli (shock, friction), and that also often
have vapor pressures which cannot be ignored beyond 50°C. The different
steps of manufacture of a case bonded grain are described in Fig. 3.
Fig. 1 1.3. Diagram of the manufacture of high energy propellants.
Ren6 Couturier
494
3 . 3 . 3. Cases preparation
3.3.3. 1. Background
Two types of cases are currently used with this type of propellant:
• metallic cases made of steel, especially designed to handle significant
pressures;
• composite cases which are increasingly used for high-performance appli-
cations.
These cases are, of course equipped with thermal protections and coated with
a liner, a material for binding with the propellant.
3.3.3. 2. Installation of the inert materials
Because the installation process of the various inert materials is described
in detail in Chapter 13, this section will provide only a succinct list of the
operations sequence necessary to prepare a metallic-type case to receive the
propellant slurry. These operations include:
• surface treatment of the cases;
• bonding of the thermal protections;
• coating of the entire surface with a liner.
The process selected for the coating depends both on the nature of the liner
and on the shape of the case. Spraying techniques, however, are most widely
used.
The quality of these coatings is fundamental for a good adhesion of the
liner to the propellant, and of capital importance for the reliability of the
propellant grain.
To improve the bonding characteristics (tensile, shear, and peeling
strength) between the liner and the propellant, we may have to resort to the
use of embedding agents of very specific shapes inside the liner (for example,
granules with a cellulosic derivative base), that will function as so many
mechanical embedment points for the propellant.
3. 3. 4 . Ra w materials preparation
With the exception of energetic binders (nitroglycerine, butanetriol trini-
trate, etc.) which require special handling, the other raw materials do not
have to be treated or transformed before use. After acceptance according
to a determined procedure, the raw materials are stored by homogeneous
manufacture batches in the environmental conditions — temperature,
humidity — required for their specific nature.
As for the energetic plasticizers, there are several possibilities, according to
Advanced Energetic Binder Propellants 495
the manufacturing processes selected for the propellants and the availability
of the mass production of nitrate esters:
• Use of pure nitrate ester, which is possible when a production facility or
dynamite extraction facility are located close to the propellant plant. This
allows a rapid mixing of the energetic plasticizer with the prepolymer to
form a desensitized premixture which can then be stored, i.e., from the
time it contains a chemical stabilizer.
• Use of nitrate ester diluted with a volatile solvent (acetone or methylene
chloride type) or an inert plasticizer (triacetin type). These solutions are
used if the nitrate esters production facilities are located far from the
propellant production facilities, or when the manufacturing process
requires it.
3. 3. 5. Manufacture of propellant slurries
The principle of propellant slurry manufacture is based almost exclusively
on the preparation of a binder with low viscosity in which the fillers are
incorporated. After its homogenization in the suitable mixer, the slurry must
maintain a certain level of viscosity to allow its casting by pouring or
injection, for as long as the industrial process requires it.
The sequence of incorporation of the propellants ingredients is the result of
a trade-off that takes into account, for example:
• evolution of the slurry’s viscosity;
• safety problems, related to the use of liquid nitrate esters and/or the use of
powerful oxidizers/fuel mixtures such as ammonium perchlorate and
aluminum.
Furthermore, it is necessary during this particular phase to maintain very low
levels of humidity to facilitate the development of urethane linkages (reaction
of isocyanates with alcohols), thereby ensuring good propellant mechanical
properties.
For the purpose of illustrating one of the possible manufacture plans, we
will use a propellant that contains the following constituents:
Binder
Prepolymer with a tailored molecular weight, polyester or polyether type;
Nitrocellulose (used in low ratios as a crosslinker);
Nitroglycerine;
Stabilizer.
Charges
Nitramine (HMX or RDX);
Ammonium perchlorate.
496
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Curing agents
Polyisocyanate;
Cosslinking catalyst.
The sequence of the operations necessary to obtain a homogeneous slurry
can be summarized as follows:
• First, a premix is prepared, containing the prepolymer in which the
stabilizer and the nitrocellulose are solubilized.
This operation takes place at atmospheric pressure and at a specific
temperature which must take the melting temperature of the prepolymer
into consideration.
• Pure nitroglycerine or nitroglycerine in solution is added to this premix.
This operation takes place under slight agitation, and at a moderate
temperature. Once the energetic plasticizer is completely incorporated,
the whole is placed under vacuum, still at a moderate temperature, and is
subjected to a degassing, under slight agitation, to ensure both the
homogenization and the dwelling of the premix. When the nitroglycerine
is introduced as a solution, the degassing operation also permits the
removal of the solvent.
• At the end of this operation the curing agent is added. The binder is then
ready to receive the solid charges.
• In this particular case the nitramine (RDX or HMX) and the ammonium
perchlorate may be introduced in the mixer, either consecutively or in
sequenced phases. The tailoring of the incorporation procedure must take
into account the various particle sizes that are used in order to avoid
problems of unwanted increase of the viscosity of the slurry.
At the industrial level, it is preferable to have a system permitting a
continuous introduction of the charges. Such a facility includes one or several
hoppers, located above the mixer, containing the various fillers; the charges
are fed to the mixer through a vibrating band.
• After the various charges have been incorporated, the mixing of the whole
continues at moderate temperature — usually between 40 and
60°C — (under dynamic vacuum pressure below 50 mmHg), with the
same goal, i.e. to maintain a humidity level on the slurry that is as low as
possible. Approximately 1 hour before the completion of the mixing, the
crosslinking agent is introduced into the slurry. From that moment on
the polymerization has been started, and the viscosity of the slurry will
keep evolving
Vertical mixers are particularly well suited for the manufacture of XLDB
slurries because they allow:
• from a quality point of view, a good homogenization of the fillers in the
binders;
Advanced Energetic Binder Propellants 497
• from a safety handling point of view, a significant decrease in the risks of
diffusion of nitrated oils in the bearings.
3 . 3 . 6 . Production of propellant grains (casting,
curing, finishing and quality controls)
Casting, curing and finishing operations leading to the production of the
propellant grains are comparable to those described in Chapter 10 on
composite propellants. However, some adjustments were necessary to accom-
modate the presence of explosive charges (nitramines) and, particularly, of
energetic plasticizers (nitroglycerine, for example), which are sensitive to
mechanical stimuli, have a limited thermal stability, and are likely to migrate.
Among the specific adjustments carried out, we may mention:
• use of specific valves preventing shocks and frictions;
• design of fluid-tight equipment, which keeps handling to a minimum — in
this regard, integral molding is recommended because it cuts out all
finishing operations;
• a greater control of the temperature of the curing facilities, to avoid any
change likely to cause a decomposition of the nitrate esters.
Finally, the quality controls include those done on composite propellants,
complemented by specific tests, such as chemical stability, and thermal
behavior (cook-off tests).
4. Characterization of Advanced Energetic
Binder Propellants
4.1. PHYSICAL AND PHYSICOCHEMICAL CHARACTERISTICS
4.1.1. Density
Depending on the nature and the fillers content, advanced energetic
propellants present a wide range of densities (Table 6).
XLDB, because they accept a higher total solid content than CMCDB,
naturally have higher densities.
The introduction of aluminum (p = 2.7 g/cm 3 ) in a propellant that already
contains an oxidizer (HMX + ammonium perchlorate, for instance) is anoth-
er determinant for the evolution of the densities.
4. 1.2. Glass transition temperature (T g )
The mechanical behavior of propellants may be be altered at low tempera-
tures because of structural changes in the binder (glass transition, or of the
498
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Table 6 Densities (p) available in advanced energetic propellants
Propellant type
CMCDB
XLDB
NEPE
Nature of fillers
nitramine
nitramine nitramine
nitramine
+
+
ammonium
ammonium
perchlorate
perchlorate
-(-aluminum
g/cm 3
<1.70
<1.76 <1.80
<1.88
second order). The temperatures at which these transitions occur depend
primarily, for a specific polymer, on the content level and the nature of the
plasticizer (Fig. 4). In fact, in the case of nitrocellulosic binders, they tend
toward the second-order transition temperature of the plasticizer when the
plasticizing ratio increases [6]. We must remember that the second-order
transition temperature of nitroglycerine, when it remains at superfusion, is
close to — 65°C.
In the case of XLDB binders, which are highly plasticized, the glass
transition temperatures typically range between — 55°C and — 60°C, which
Fig. 1 1.4. Evolution of the glass transition temperature (Tg) of nitrocellulosic binders
versus the amount and the nature of the plasticizer.
Advanced Energetic Binder Propellants 499
explains the good levels of elasticity of this propellant family as far as — 40°C
to - 50°C.
4.1.3 . Thermal expansion coefficient (a)
The binders of propellants have thermal expansion coefficients (a) that are
greater than those of the charges. Therefore, the higher the fillers content, the
more a will have a tendency to decrease.
Additionally, in the case of energetic binder propellants, the plasticizer
usually shows the greatest variations of volume versus temperature. Conse-
quently, the more the binder is plasticized, the more a will have a tendency to
increase.
Based on these observations, the thermal expansion coefficients of XLDB
propellants, measured above the glass transition point, usually range from
1.00 x 10 -4 to 1.30 x 10“ 4 K _1 .
4.1.4. Crystallization of energetic plasticizers
In some cycles of low temperature conditioning, XLDB propellants with
nitroglycerine base and crosslinked CMCDB (or EMCDB) with high plasti-
cizing ratio may exhibit an embrittlement phenomenon, detrimental to the
operational reliability of the propellant grains. Such embrittlement, which is
manifested by a total or partial loss of the elastic properties of the material, is
the result of the crystallization of the energetic plasticizer inside the propel-
lant [7,8].
Research done on the crystallization of liquid nitrate esters has provided
the following information [7]:
• pure nitrate esters do not crystallize easily;
• crystallization is facilitated through seeding with foreign matter that may
be present in the propellant;
• once it has been initiated, the kinetics of crystallization depend on the
temperature — with nitroglycerine, for example, the kinetics of crystalline
growth has its highest value at around — 5°C (Fig. 5).
Energetic plasticizers may be differentiated through their ability to crystal-
lize; nitroglycerine, for example, crystallizes faster than triethyleneglycol
dinitrate or butanetriol trinitrate:
• use of specially designed nitrated oils delays or suppresses the crystalliza-
tion phenomena [7-9].
As far as quality controls are concerned, energetic binder propellants are
subject to isothermal conditioning at low temperatures (between 0 and
— 50°C) or are exposed to daily arctic cycles, for example — 12°C — 40°C,
500
Ren6 Couturier
Fig. 11.5. Progress of the crystallization front on nitroglycerin specimens at varying
temperatures (readings made one hour and two hours after conditioning).
which are more severe because they facilitate the crystalline germination-
growth sequences.
Table 7 gives a description of the behavior at low temperature of two
XLDB propellants, one plasticized with nitroglycerine and the other with a
mixture of nitrate esters. The propellant containing the nitrate esters resists
crystallization, i.e. its mechanical properties are not affected at low tempera-
ture, while the propellant containing nitroglycerine becomes embrittled
within 10-15 days, depending on the type of conditions selected.
4.2. MECHANICAL PROPERTIES
Depending on the type of grain selected (free-standing or case-bonded), the
mechanical characteristics required of the propellant are different:
• Free-standing grains: the propellant is free to deform. The mechanical
strains involved mainly concern storage and firing. As far as the material
is concerned, sufficient elastic modulus values must be ensured, particu-
larly at high temperatures in the case of tactical missiles.
• Case-bonded grains: the propellant is bound to the case. Its mechanical
properties must be tailored to the thermal stress/strains that occur at
cooling, right after curing, and for the remainder of the life of the rpcket
motor. The strain resulting from deformation occurring at firing must
also be taken into account.
To be suitable, the propellants must be capable of handling a good level of
strain in the entire range of temperatures met during operational conditions
Advanced Energetic Binder Propellants
501
Table 7 Low temperature cycling of XLDB propellants (fillers = 70%) evolution of the
strain at maximum stress ( e m )
XLDB
Nature of the propellant
Nitroglycerine
Nitrate ester mixtures
Cycling conditions :
Isotherm:
-15°C
— 30°C
Crystallization after 15 days
Crystallization after 15 days
No crystallization after 6 months
No crystallization after 6 months
Daily arctic cycle
— 12 <= — 40°C
Crystallization after 10 days
No crystallization after 6 months
4. (%) at — 40°C
Crystallized propellant
-2%
Non-crystallized propellant
- 22%
of the grain. In the case of tactical missiles it is particularly important to
maintain a good trade-off between the strains at cold temperatures and the
values of maximum stress ((x m ), and of the Young’s modulus at high
temperatures.
These mechanical considerations, related to the design of the grains,
determine largely the areas of application of CMCDB/EMCDB propellants
and XLDB/NEPE propellants:
• Non-crosslinked CMCDB propellants exhibit a good stress level under
high temperatures, but the level of strain at cold temperatures is not
suitable for use in case-bonded grains. As a result they are mainly used for
the production of free-standing grains.
For these propellants, however, there is a possibility of extending their use to
case-bonded grains, in as much as it is possible to increase the plasticizing of
the nitrocellulosic binder, involving a strengthening of its network through
crosslinking (EMCDB):
• XLDB propellants all exhibit good levels of elongation (including under
low temperatures) and satisfactory stress at high temperatures. Conse-
quently, they are well-suited for the production of case-bonded grains.
Mechanical characterizations performed on propellants
A systematic control of mechanical tensile properties is done on all
propellants manufactured, first at ambient temperature, and if necessary at
low temperature ( — 40°C, — 50°C) and high temperature (approximately
-h60°C) for propellants intended for tactical applications. For a more
detailed characterization, other tests are performed:
• Uniaxial tensile test, at various rates (from 0.5 to 500 mm/min, for
example) and various temperatures. Experimental data permit the plot-
ting of master curves necessary during the design of the propellant grain.
502
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• Behaviour at creeping, and at relaxation.
• Simultaneous measurements of the volume variations during a tensile
test, recorded with a gas dilatometer. This technique is well suited for the
determination of the characteristics of the adhesion between binder and
fillers.
4.2.1. Mechanical behavior of CMCDB
propellants
Mechanical properties of the different CDB propellants occur during the
curing operation, at the time when the casting solvent diffuses into the
powder granules, which swell and bond to each other. The more the casting
powder is plasticized, the better this diffusion will be. With curing tempera-
tures of the order of 50-65°C, the mechanical properties stabilize within 2-4
days.
4.2. 1. 1. Influence of the plasticizing ratio
The possibility, on the one hand, of introducing a plasticizer in the casting
powder, and on the other hand, of adjusting the casting powder/casting
solvent ratio during the filling of the mold, provides the capability of
obtaining propellants with a wide range of mechanical properties.
Let us take the case of a casting powder containing 45% of solid charges:
up to 30% of nitroglycerine can be introduced, in place of the nitrocellulose.
This substitution causes a variation in the plasticizing level (plasticizer/
plasticizer + polymer) of the propellant of approximately 50-80%. In terms
of the mechanical properties, it is manifested by:
• a decrease of the values of the maximum stress o m at all temperatures;
• an increase of the strain values at low temperatures.
Figure 6 illustrates the evolutions of o m and e m for various plasticizing ratios.
At 65-70 % the level of maximum stress cr m at + 65°C usually drops to values
lower than 0.5 MPa. This may mean that it is no longer acceptable for a
propellant grain, and it becomes necessary to crosslink the nitrocellulosic
network in order to strengthen the mechanical properties of the propellant.
4.2. 1.2. Influence of fillers
The quality of coating by the nitrocellulosic binder is a critical element of
the mechanical properties of the finished propellant. As with XLDB or
composite propellants, it is necessary to optimize the rheological properties
of the binder, and the particle size distribution of the fillers. In addition, the
quality of the binder-charge adhesion depends also on the nature of the
charge. Figure 7 illustrates the volume variations AF/F recorded with a
Advanced Energetic Binder Propellants
503
10
4
60
RDX Content in the
casting powder
o
- -30°C
o
✓ y - ^
' 0
65
70
• 45 %
o 47.5 %
▼ 50 %
-40°C
Plasticizing Ratio (%)
2
03
Q.
5
E
c n
1
0.5
60
nA
V +20‘C
‘^+ 60 °C
Plasticizing Ratio (%)
Fig. 1 1.6. CMCDB propellants. Evolution of a m and e m in function of the plasticizing
ratios.
Farris gas dilatometer for two CMCDB propellants, one loaded at 30% with
ammonium perchlorate, the other at 30% with RDX. It turns out that
the ammonium perchlorate compositions exhibit a better binder-charge
adhesion than those loaded with nitramines with identical particle sizes; de-
wetting occurs only at higher strains, and the total volume variation AV/V
is clearly smaller.
4.2. 1.3. A special case: EMCDB propellants
With plasticizing ratios greater than 65-70% it is necessary to crosslink the
nitrocellulose to strengthen the maximum stress (cr m ) of these advanced CDB
propellants at high temperatures. The strain values at low temperature of the
resulting propellants are improved, and they may be used in case-bonded
grains.
Reinforcement of the polymeric network may be obtained:
504
Rene Couturier
Fig. 11.7. Farris ga, iilatometer behavior of CMCDB propellants loaded with 30%
ammonium perchlorate (A) or 30% RDX (#).
• either by direct crosslinking of the nitrocellulose;
• or by crosslinking the nitrocellulose with small percentages of hydroxy-
terminated prepolymer (preferably polyester) — this prepolymer is intro-
duced in the casting powder or dissolved in the casting solvent before
casting.
Small percentages of bi-functional isocyanates are sufficient to obtain an
increase in the strain capabilities at high temperatures. Optimization is
obtained with NCO/OH ratios lower than 0.1.
The values indicated in Table 8 for the mechanical properties of EMCDB
Table 8 Influence of crosslinking on the mechanical properties of EMCDB propellants
containing 30% RDX
Plasticizing ratio
76%
81%
No
Direct
NC crosslinked
Direct
crosslinking
crosslinking
with
crosslinking
of NC*
of NC
prepolymer
of NC
<r m (MPa) at + 60°C
0.12
0.70
0.60
0.45
«»(%) at — 40°C
25
20
28-30
40
* NC = Nitrocellulose
Advanced Energetic Binder Propellants
505
propellants with 30% RDX demonstrate the advantage of crosslinking for
increasing the <r m stress capabilities at 60°C and the advantage of the
prepolymer for the improvement on strains at — 40°C.
4.2.2. Mechanical behavior of XLDB and NEPE
propellants
Mechanical properties of these propellants are also obtained after curing,
since this phase is designed to activate the crosslinking process of the binder.
The final mechanical properties depend on the composition of the binder,
on the fillers incorporated in that binder, and on the manufacturing condi-
tions. Special attention had to be given to the characteristics of the binders of
XLDB propellants due to their high contents of plasticizer (up to 70-75%).
4.2.2. 1. Characterization of XLDB binders
Studies of the elaboration of XLDB binders have demonstrated the
influence of formulation parameters such as: nature of the plasticizer and of
the prepolymer, and nature of the isocyanates and of the crosslinking
catalysts.
On the basis of crosslinking density measurements, the following tenden-
cies can be observed:
• an increase of the plasticizing level contributes to a decrease in the
crosslinking density, which tends to drop significantly when the plasti-
cizer/polymer ratio is close to 3;
• a decrease is also recorded when the molecular weight of the prepolymer
increases;
• the incorporation, as crosslinker agents, of polyols with high molecular
weights (nitrocellulose and cellulose acetobutyrate, for example) improve
the crosslinking density;
• the crosslinking density is optimal when the ratios NCO/OH are slightly
greater than the stoichiometry;
• There is a fairly good concordance between the crosslinking densities of
the binders and their mechanical properties. It has been possible to
establish a linear relationship between these two parameters for simple
systems with a polyoxyethyleneglycol or glycol polyadipate base [10].
4.2.2.2. Influence of fillers
As with all composite structures, the mechanical properties are tied to the
interaction between the binder and the charge. When there is a transfer of
stresses from the binder to the fillers, these function as a physical reinforce-
ment, causing an increase of the modulus, and at the same time a decrease in
506 Rene Couturier
Table 9 Mechanical properties evolution of XLDB propellants as a function of the total solid
content
Solid content (%)
65
70
70
Plasticizer content (%) (binder)
71
71
74
(MPa)
+ 20°C
1.0
0.8
0.7
+ 60°C
0.8
0.6
0.6
«.<%)
+ 20°C
180
130
130
— 30°C
150
100
110
— 54°C
23
16
18
the elongations. The loading capability of binders is limited, however, and
these limits particularly depend on the nature of the polymer, the plasticizer
content and the nature of the fillers. Table 9 indicates some typical, cr m stress
and e m strain values for XLDB propellants with a polyester binder with
various total solid contents.
As with composite propellants with a polyurethane binder, the optimiza-
tion of the mechanical properties requires:
• the adaptation of the particle size of the various selected solid fillers;
• the control of the humidity levels, which must remain as low as possible.
Some fillers may have an influence on the elaboration of the polyurethane
networks plasticized with nitrate esters. This occurs in particular with
ammonium perchlorate, which has a low solubility in the prepolymers rich in
ether links such as polyoxyethyleneglycols (PEG). The result in the corre-
sponding propellants is a decrease in the maximum stresses (cr m ) at ambient
temperature.
4.2. 2. 3. Conditions for propellant curing
The curing conditions (time, temperature) are determined by the stabiliza-
tion of the mechanical properties. For case-bonded grains the lowest possible
curing temperatures are always sought in order to reduce the thermal stresses
due to cooling. Based on the type of propellant, the curing temperatures
range from 40 to 60°C and the curing times necessary for the stabilization of
the mechanical properties range from approximately 10 to 12 days.
4.3. BURNING RATE OF ADVANCED ENERGETIC BINDER
PROPELLANTS
4.3. 1. Burning rate of CMCDB propellants
CMCDB propellants need to be considered as an extension of the double-
case propellant family. Therefore, the adaptation of their characteristics is
Advanced Energetic Binder Propellants 507
done by modifying the characteristics of the binder, using the ballistic
modifiers available for these DB propellants.
The introduction of nitramines in these binders compensates more or less
for the effects of the “super-rate” caused by the presence of burning rate
modifiers. K. Sumi and N. Kubota [11] describe the negative effect of
increasing amounts of HMX in a propellant catalyzed with lead salicylate/
ethyl-2 lead hexanoate; the plateau effect disappears for amounts higher than
about 27%.
In general, less spectacular effects are recorded, which are manifested
particularly by a decrease in the level of the burning rate; the plateau effects,
although less marked, are nevertheless quite correct for fillers contents up to
40%. There are even ballistic modifiers based on lead or copper salts that
remain virtually insensitive to the amount of nitramine [12]: retention of the
plateau effect, a very small decrease of burning rate at the plateau (Fig. 8),
retention of good temperature coefficient ( < 0. 1 5 % per °C), and possibility of
regulating the burning rate with well-known additives such as carbon blacks.
4. 3. 1.1. RDX-HMX comparison
Slightly less good burning characteristics have often been observed,
experimentally, when HMX replaces RDX: lower burning rate, less marked
plateau effect, and a temperature coefficient which is not quite as low.
K = 300
e = 2crc
5
— • CB = 0.5
•CB = 0.3
’• CB = 0.2
• CB = 0.1
• •— CB = 0
20
27
31
i
34
RDX (%)
38
41
Fig. 11. 8. Burning rate of CMCDB propellants as a function of RDX percentage for
different content of carbon black (CB).
508
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20
(/>
E
E
-D
10
_J 1 1 1 —
1 0 15 20 30
Pressure (MPa)
Fig. 11.9. Influence of ammonium perchlorate content on the burning rates of
CMCDB propellants catalyzed with lead aromatic ballistic modifier.
4.3. 1.2. Influence of ammonium perchlorate
Introduced in catalyzed CMCDB or EMCDB propellants, ammonium
perchlorate causes the destruction of the plateau effect, even in very small
amounts (Fig. 9).
4.3.2. Burning rate of XLDB and NEPE
propellants
4.3.2. 1. Nitramine based XLDB propellants
In his synthesis paper, R. A. Fifer points out the difficulties and the few
solutions available to affect the burning rate of a propellant with a high
content of nitramine [13]. As for the rare catalysts mentioned in the
literature, they are not particularly efficient [3,14-16].
Although it is possible to modify the burning behavior of the most widely
used binders based on prepolymers of the polyether or polyester type, highly
plasticized with nitrate esters, the range of burning rates available remains
fairly limited because of the presence of a high amount of nitramine (greater
than 50%) [17].
Measures designed to modify the decomposition mechanism of nitramines
(RDX or HMX) have not yet succeeded in providing solutions that are
applicable industrially.
Advanced Energetic Binder Propellants 509
To sum up, the burning rates of XLDB propellants range from 2 to 15 mm/s
at 7 MPa. The pressure exponents are situated between 0.35 and 0.60 and the
temperature coefficients are very similar to those of composite propellants ( 7 t k
from 0.15 to 0.35% per °C).
Remark
Research for any new ballistic modifiers implies that a propellant feasibility
study be done at the same time. This is due to the fact that some additives,
particularly those with a lead base, turn out to be efficient crosslinking
catalysts, which may make their use incompatible with mass production.
4.3.22. XLDB propellants with nitramine and ammonium
perchlorate
Ammonium perchlorate acts as a very efficient ballistic modifier. It is
possible to regulate the burning rate over a wide range by varying both the
content and the particle size of the oxidizer. Figure 10 gives an idea of the
evolution of the burning rate as a function of the evolution of the ammonium
perchlorate-octogen proportions in a propellant with a 70% total fillers
content.
In addition to the usual role played by the particle size and the amount of
ammonium perchlorate, we may also note that:
25
<n
£
£
20
12
—I I L_
14 16 18
nh 4 cio 4 (%)
Fig. 11.10. XLDB propellant loaded with 70% fillers (HMX-Ammonium perchlor-
ate). Evolution of the burning rate as a function of ammonium perchlorate content
(particle size = 10 n m ).
510
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• Polyether binders tend to lead to burning rates that are higher than those
obtained with polyester binders.
• Pressure exponents have a tendency to decrease when the ammonium
perchlorate content increases. They decrease more rapidly when the
particle size of the oxidizer is smaller, reaching minimum values which
also depend on the size of the ammonium perchlorate particles. With fine
ammonium perchlorate (3 pm), the exponent is around 0.50-0.55, while
with somewhat larger perchlorate (10 pm), the exponent may drop to as
low as 0.45.
4.4. ENERGETIC CHARACTERISTICS
4.4 . 1 . Recapitulation of theoretical performances
Specific impulse ( I s ) and volumetric specific impulse (7 s .p) theoretically
attainable with these propellants are shown in Table 10.
7 S and 7 s .p evolve differently according to the nature of the solid charges
incorporated in the binders:
• If the filler is a nitramine, 7 S and 7 s .p increase in a virtually linear manner
when the amount of RDX or HMX increases. Because RDX and HMX
have closely related thermodynamic characteristics, the substitution of
one by the other has little incidence on the values of 7 S . But the difference
shows up in the value of the volumetric specific impulse, due to the fact
that the density of RDX is lower than that of HMX: respectively 1.818
and 1.903 g/cm 3 .
• A combination of ammonium perchlorate with a nitramine allows a gain
in performance provided, however, that the proportions are optimized as
a function of the nature of the binders used (Figure 11).
Incorporation of metallic fuel, such as aluminum, combined with an
oxidizer (perchlorate ammonium + nitramine) allows to obtain high 7 S and
Table 10 Theoretical performance obtainable with advanced energetic binder propellants
Nature of fillers
Nature of the
propellant
/ s (s)
/ s .p (s.g.cm" 3 )
Nitramine
XLDB
CMCDB*
EMCDB
250
245-250
440
415-425
Nitramine + ammonium perchlorate
XLDB
260
465
Nitramine + ammonium
perchlorate + aluminum
NEPE
275
515
* The values of / s and / s .p increase when the propellants are crosslinked, due to the presence
of high amounts of nitrate esters in the nitrocellulosic binder.
Advanced Energetic Binder Propellants
511
Fig. 11.1 1. Evolution of / s as a function of the HMX/Ammonium perchlorate ratios
for XLDB propellants with 70% solid fillers whose binder is plasticized either with
nitroglycerine, or triethyleneglycol dinitrate.
I s .p values. As in the case with composite propellant, it is necessary, however,
to optimize the proportions of the various charges to obtain the maximum
performance. The optimum content of aluminum for NEPE propellants
ranges between 15 and 20%.
4. 4. 2. Measured performance
The experimental measurements of specific impulse are done on standard-
ized reference grains during a bench firing test. The propellant grains used
have a radial combustion.
The specific impulses measured reveal a shortfall in comparison with the
computer predictions, which do not take into account the various losses
resulting from the nature of the grain and the firing conditions.
Furthermore, the presence of a metal such as aluminum creates a problem
of combustion efficiency (due to the influence of the particle size, of the
amount of fuel, the influence of the firing conditions and the size of the
grains). Table 11 shows clearly that the shortfalls between theoretical / s and
measured I s are greater with aluminized propellants.
4.5. FUNCTIONAL CHARACTERISTICS
4.5.1. Signature
Grain signature is assessed on its ability to produce smoke (primary or
secondary) or afterburning phenomena (re-ignition of the combustion gases).
512
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Table II Theoretical and measured performances of several typical advanced energetic
binder propellants
Propellant
CMCDB
XLDB
NEPE
Nature of fillers
RDX
HMX
HMX
H-
H-
ammonium perchlorate
ammonium perchlorate
+
aluminum
Theoretical / S (s)
(expansion 70/1)
241
257
270
Measured / S (s)
229
245
249
A/ S (s)
12
12
21
Standard motor
Mimosa
Bates 12"
Bates 12"
diam. = 203 mm
diam. = 305 mm
diam. = 305 mm
L = 1 000 mm
L - 508 mm
L = 508 mm
Such phenomena, which may affect either the guidance or the detection of the
missile, or of the combat platform, are discussed in detail in Chapter 5.
The importance of the signature of advanced energetic binder propellants
depends primarily on the nature of the fillers incorporated in the propellant
(Table 12).
The ability of these propellants to generate smoke and flashes is examined
in the following sections.
4.5.1 .1 . Primary smoke
Usual energetic binders consisting of atoms C, H, O and N, do not generate
primary smoke. This is also true for the oxidizers contained in these binders
(RDX, HMX, or ammonium perchlorate). As a result, the release of primary
smoke by CMCDB or XLDB propellants is mainly tied to the presence of
additives carrying metallic atoms which are incorporated in the propellant to
Table 12 Classification of advanced energetic binder propellants as a function of their ability
to generate smoke
CMCDB
EMCDB
XLDB
NEPE
Fillers
Nitramine
Nitramine
Nitramine
4- ammonium
perchlorate
( < 20%)
Nitramine
+ ammonium
perchlorate
+ aluminum
Classification
Smokeless
Smokeless
Minimum smoke
Smoky
Advanced Energetic Binder Propellants 513
respond to a specific operational requirement. These additives, of which only
small amounts are incorporated, include:
• ballistic modifier (lead and copper salts, for example);
• damping particles, sometimes required in some radial burning grains;
• afterburning suppressants including an alkaline ion (most often potas-
sium) which decompose during combustion but may give rise to recom-
binations in the gaseous phase, which is detrimental to the signature.
4.5. 1.2. Secondary smoke
Secondary smoke is characteristic of propellants that contain ammonium
perchlorate. The formation of H 2 0/HC1 aerosols depends, on one hand, on
the atmospheric conditions (temperature and relative humidity), and on the
other hand, on the amount of NH 4 C10 4 in the propellant.
4.5. 1.3. Afterburning
Afterburning phenomena can be suppressed by the introduction of addi-
tives with alkaline metals base (sodium and particularly potassium: K 2 S0 4 ,
KN0 3 , K 3 A1F 6 and others).
When developing new propellant compositions, however, the choice of an
additive must take into account not only its specific afterburning suppressant
function, but also such criteria as: influence on the feasibility, ballistic
properties, chemical and thermal stability of the propellant, as well as the
possible effects on the exhaust plume (primary smoke).
4.5.2. Combustion instabilities
Instabilities, longitudinal as well as transverse, which are typically ob-
served in radial burning grains, are the subject of theoretical research so that
computer codes may be developed for predictive analyses (Chapter 4).
This is an interesting approach, in as much as it should allow the reduction
of the number of lengthy and expensive tests that need to be performed,
particularly in the case of large rocket motors. For modest-size grains
destined for tactical purposes, on the other hand, it is possible and even useful
to define experimentally the stable combustion zones.
4.5.2. 1. Conditions for occurrence of transverse instabilities
In a given propellant, the occurrence of combustion instabilities is tied, on
one hand, for the firing conditions, and on the other, to the design of the
propellant grains.
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514
(a) Firing conditions
Pressure is a dominant factor. Instabilities usually occur at low pressures,
the oscillations increase as the pressure decreases. For a given pressure, the
firing temperature may also affect the triggering of instabilities.
(b) Geometry of propellant grains
Starting from free-standing grains with a constant diameter (£)), there is a
grain length (L) above which combustion instabilities occur. Conversely,
starting from grains with a constant length (L), it is possible to determine an
initial central port diameter ( D ) above which the combustion will be stable.
Finally, the combining of these different experimental firing tests allows
one to obtain a more accurate definition of the grains size (Fig. 12).
4.5.2. 2. Function of damping particles
Damping of the pressure oscillations in the combustion chamber can be
obtained through the presence of solid particles in the combustion gases. For
each specific vibration, there is a proper particle size.
L/D = 12
Fig. 11.12, Identification of a stable combustion zone as a function of the dimen-
sional characteristics of the propellant grain. CMCDB propellant with 30% RDX.
Advanced Energetic Binder Propellants 515
When the grain is being designed, there are two ways of proceeding:
• By introducing metallic additives (aluminum or tungsten, for example)
which, when they burn, generate oxidation condensed products (A10 3 ,
W 2 0 3 , etc.). This is the most widely used solution, but it does not afford
the possibility of controlling the size of the particles that are generated.
• By introducing refractory additives with melting points that are higher
than the combustion temperature of the propellants. This allows a better
optimization of the size of the damping particles, provided that the
vibration frequencies of the grain are known. The damping particles that
can be added to CMCDB or XLDB propellants belong to the families
of oxides (Si0 2 -Zr0 2 -Al 2 0 3 for example), carbides (SiC-ZrC-BC),
or nitrides.
When it becomes necessary to have recourse to the introduction of an
additive to stabilize the combustion of a grain, the consequences on the other
properties must be ascertained, such as:
• Performance : the metals (aluminum, for instance) contribute to raising
the specific impulse; refractory products, on the other hand, are rather
detrimental.
• Burning rate : these additives may cause perturbations of the burning rate-
pressure law, particularly with CMCDB and XLDB propellants which
contain catalysts common in double-base propellants.
• Signature : the solid particles released in the exhaust plume are respons-
ible for primary smoke.
4.6. AGING
Aging behavior of propellant grains depends not only on the nature of the
propellant, but also on the environmental conditions (temperature, and
relative humidity, for example). For the propellant, this aging translates into
an evolution of the chemical and/or physicochemical characteristics, which
may in turn alter its mechanical and ballistic properties, as well as its safety
behavior. Table 13 enumerates the major consequences related to these
evolutions.
4 . 6 ‘ 1 . Chemical stability
The presence of nitrate esters in advanced energetic binder propellants
requires, as with all double-base propellants, the incorporation of stabilizers
whose function is to trap the nitrogen oxides resulting from the decomposi-
tion of the nitrates.
The stabilizers used for CMCDB and XLDB propellants that contain no
ammonium perchlorate are often the same ones used for homogeneous
516
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Table 13 Consequences of aging on the properties of advanced energetic binder propellants
Type of evolution
Nature of the evolution
Consequences and
properties affected
Chemical
Decomposition of nitrate esters
♦ Chemical stability
(consumption of stabilizer)
Explosive behavior
(risk of ignition)
♦ Physical integrity (cracks)
^Operational safety
Evolution of the polymer network:
rupture of chains, creation of links
Crosslinking density
Mechanical properties
Physicochemical
Mobility of the energetic plasticizer:
migration, exudation, volatilization
Composition of the material
| ♦Mechanical properties
Ballistic properties
♦ Explosive properties
Binder-charge adhesion
Mechanical properties
Crystallization of the plasticizer
(cycling at low temperatures)
Mechanical properties
^ Explosive properties
propellants: 2-nitro diphenylamine (2NDPA), and N-methyl p-nitroaniline
(MNA), for example. When they contain ammonium perchlorate, resorcinol
(or resorcinol derivatives) combined with 2NDPA is also efficient.
The mechanisms of nitrate esters decomposition, and of the oxides
interaction with the stabilizers, are described in depth in Chapter 9.
The chemical stability of advanced energetic binder propellants may be
affected by some ingredients of the binder and the nature of the fillers, as well
as by the various additives necessary for the functional characteristics of the
propellant grain.
4.6. 1. 1. Influence of the binders
• Increase of energetic plasticizer content in the binder is generally mani-
fested by a faster consumption of the stabilizer.
• The polyurethane binders plasticized with energetic nitrate esters usually
exhibit a chemical stability that is lower than those of nitrocellulosic
binders. Among the parameters that influence this stability are:
— nature of the polyisocyanates: in general, the aromatic poly isocyan-
ates give a slightly better chemical stability;
— nature of the prepolymer: prepolymers rich in ether functions lead to
less chemical stability.
Advanced Energetic Binder Propellants 517
4.6. 1.2. Influence of the fillers
• Nitramines (RDX and HMX) are chemically stable. They do not partici-
pate in a significant manner in the degradation of the advanced energetic
binder propellants.
• Ammonium perchlorate, on the other hand, plays a particular role by
modifying the decomposition mechanisms of the nitrate esters and the
interaction mechanisms of the nitrogen oxides with the stabilizers. Under
standard aging conditions (50-70°C), this is expressed by a lower
consumption of the stabilizer and lower gaseous emissions.
4.6. 1.3. Influence of the additives
Incorporation of additives in even small amounts may cause significant
modifications in the decomposition kinetics of nitrate esters. This is true in
the case of ballistic modifiers.
4, 6. 2. Cracks caused b y aging
The propensity of a grain of a specific size to crack is a function, on one
hand, of its chemical and physicochemical behavior, and on the other hand,
of its mechanical properties (refer to Chapter 9).
For propellants with similar compositions and mechanical properties,
resistance to cracks caused by aging depends mostly on the nature and the
proportion of stabilizer(s) included. It has been demonstrated, for example,
that centralite is clearly less efficient than 2-nitro diphenylamine (2NDPA).
With CMCDB or XLDB propellants it might be interesting to combine two
stabilizers that have very different nitrosation kinetics to improve resistance
to cracking.
Included among the other propellant constituents that may affect this type
of aging are:
• presence of ballistic modifiers;
• cure agents (nature, content);
• nature of the fillers. The presence of ammonium perchlorate slows down
the gases generation, leading as a result to critical sizes much larger than
those of double-base propellants or CMCDB or XLDB propellants
loaded with nitramines.
4. 6. 3. Mechanical aging
The main causes of the evolution of the mechanical properties of the
advanced energetic binder propellants are the presence of nitrate esters, the
crosslinking systems, mobility of the plasticizers, and environmental factors.
518 Rene Couturier
4.6.3. 1. Presence of nitrate esters
Nitrogen oxides issued from the decomposition of the nitrate esters have
the capability of reacting directly with the polymeric chains, or of combining
with traces of humidity present in the propellant to produce chemical species
(HN0 3 for example) which are particularly aggressive toward the polymers
(cutting by acid hydrolysis). The result is a depolymerization causing a
decrease of the Young’s modulus of the material. However, this mechanical
aging can be minimized through the presence of chemical stabilizers perform-
ing efficiently inside propellant.
4. 6. 3. 2. Curing agents
Circumstances may occur where crosslinking is not entirely completed at
the end of the curing phase. During storage the mechanical properties of the
propellants may evolve toward a slight hardening, caused by the continua-
tion of the polymerization.
In addition, the eventual formation of secondary products during cross-
linking — due to the presence of traces of humidity, for example — may have
an influence on the kinetics of self-decomposition of the nitrate esters.
4.6. 3. 3. Mobility of the plasticizers
In the course of aging, the plasticizer may migrate into the materials that
are in contact with the propellant (inhibitor, liner, etc.). The localized
depletion of plasticizer causes a hardening of the propellant. The develop-
ment of bonding materials for advanced energetic binder propellants does
not completely exclude the risks of diffusion, but does limit them to such low
levels that they do not compromise mechanical integrity near the interfaces.
4. 6. 3. 4. Environment factors
• Humidity: the humidity associated with the decomposition products of
nitrate esters accelerates the acid hydrolysis of the nitrocelluloses and
polyesters, for example. Humidity most probably also has some effect on
the quality of the binder-charge adhesion.
• Air (oxygen): aging in an oxidizing atmosphere (exposed to air, for
example) may facilitate a degradation of the mechanical properties. To
prevent this process, propellant grains may be stored in inert atmosphere,
such as nitrogen.
• Temperature: it is quite obvious that the mechanical aging processes in
ambient temperature are very slow; however, their kinetics is accelerated
whenever the storage temperatures increase.
Advanced Energetic Binder Propellants
519
In practical terms we must remember that non-crosslinked CMCDB propel-
lants have very few problems of mechanical aging. But propellants whose
mechanical characteristics are obtained by crosslinking — mainly XLDB
propellants — are more sensitive to this type of aging.
4 . 6. 4 . Ballistic aging
Advanced energetic binder propellants show no significant modification of
their ballistic characteristics over time.
The factors that could have any influence are related to modifications in
the composition of the propellant are:
• loss of plasticizer (diffusion to the inhibitors, or volatilization);
• chemical evolution of the burning rate modifiers.
4.7. SAFETY CHARACTERISTICS
4.7.1. Background
Propellants are, above all, materials for which combustion is the major
risk. However, the development of new high energetic propellant families has
contributed to the identification of techniques and methodologies to study
the safety in order to take into account:
• various manufacturing phases;
• various situations in the operational life of the propellant (such as
storage, transport, firing).
These methods provide the capability of defining the major risks that must be
considered in a given situation: combustion (hazard class 1.3) or detonation
(hazard class 1.1). The resulting analyses allow us to deduce information on
the nature of the future design of facilities, or on the protective measures
needed for personnel and the environment.
4. 7.2. Safety behavior during the manufacture of
advanced energetic binder propellants
4. 7.2.1. CMCDB propellants
(a) Behavior of the casting powders
The risks involved with casting powders are similar to those from granular
products:
520 Rene Couturier
• Starting in deflagration in a limited space, they may, under the effect
of a sudden increase in the gaseous pressure, lead to a mechanical explo-
sion of the containers, or worse, to a detonation. This is known as the
deflagration-detonation transition phenomenon (DDT).
Consequently, it is important to know these mechanisms very well in order
to design suitable storage facilities and to determine the conditions of usage
that minimize the risks.
Standardized tests allow us to measure the critical explosion heights
(CEH) and detonation height (CDH).
Generally, the CEH and CDH decrease when:
— The burning rate of the powder increases. This tendency is clearly
demonstrated in the case of casting powders containing mixtures of
HMX and ammonium perchlorate. As a matter of fact, when the
perchlorate amount increases at the cost of the nitramine, the
burning rates increase while the CDH values drop (Fig. 13).
— The proportion of explosive materials (nitroglycerine -f nitramine)
increases. In fact the CEH and CDH values are more sensitive to a
variation in the amount of nitrate ester than that of nitramine.
— The size of the casting powder grains decreases.
• The French Card Gap Test also evolves with the size of the granules in a
given composition. When the diameter changes from 0.8 to 2.0 mm, the
Fig. 11.13. Evolution of the detonation critical height of casting powders as a
function of the ammonium perchlorate-HMX ratio.
Advanced Energetic Binder Propellants
521
400
-g 300
to
Q 200
100
I i i 1 ►
0.5 1 2
Diameter of the granules (mm)
Fig. 11.14. Behavior of french card gap test of casting powders containing 10%
nitroglycerin and 15% RDX.
gap drops from 300 to approximately 150 cards (Fig. 14). With granular
products the high values of gap may be the result of a deflagration to
detonation transition and not the result of a shock to detonation
transition, which is the normal case. Indeed, for a weak shock wave, there
is no detonation initiation, but only in deflagration; it is this deflagration
which later takes on a detonation regime.
• The sensitivity of casting powders loaded with nitramines to mech-
anical stimuli such as shock or friction does not evolve much with the
total solid contents.
• Casting powders may be sensitive to electrostatic discharge if they are not
graphitized. To make them perfectly conductive, however, the glazing
must be perfect.
A poor distribution of the graphite, often due to a poor surface aspect of
the granules, may result in the electric conductivity having virtually no effect.
4.7. 2.2. XLDB and NEPE propellants
(a) Premixes behavior
Premixes based on polymers and nitrate esters are sensitive to mechanical
stimuli, and in particular to shocks. Their behavior is closely related to that of
casting solvents, which is to say that they may manifest two detonation
regimes (low and high speed), according to the type of stimulus.
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522
(b) Slurries behavior
The behavior of homogenized slurries at the end of the mixing phase is
fairly close to that of finished propellants after curing, as far as mechanical
stimuli and propensity to detonate are concerned.
For propellant slurries with solid contents adapted to mass production, it
can be observed that:
• these slurries generally exhibit no violent reaction to a 30 kg drop
hammer test, below 4 m;
• use of ammonium perchlorate results in an increase in the sensitivity of
the slurries to friction — moreover, depending on the nature and the
amount of oxidizer, the same behaviour as the most sensitive composite
propellants can be found;
• gap of slurries after mixing, measured with the French gap test, is below
240 cards.
4 . 7 . 3 . Safety behavior of propellant grains
• The gap values, at the French gap test, of advanced energetic binder
propellants, are less than 180 cards. These non-confined propellants can
be given in the 1.3 hazard classification — the major hazard being
combustion — of the French law. Double-base propellants which, we
should remember, have been used around the world for over tens of years
without any problems, have gap values of around 100 cards. The increase
of gap values compared with those of double-base propellants results
from the incorporation of explosive fillers, and more precisely nitramines.
As for the conditions of detonation triggering of propellant grains, they
have been discussed in detail in Chapter 7. Transition phenomena such as
deflagration to detonation or shock to detonation generally imply a prior
fragmentation of the propellants. Propellants with good mechanical proper-
ties are therefore necessary to allow a minimization of these hazards. In this
regard, XLDB propellants, which are designed for use as case-bonded grains,
have an excellent mechanical behavior and naturally have a good resistance
to fragmentation.
• CMCDB and XLDB propellants, loaded with moderate amounts of
nitramines, are not sensitive to friction (behavior identical to that of
double-base propellants). The somewhat more greater sensitivity of
XLDB propellants comes for the most part from the higher content of
nitramines ( > 60 %). Ammonium perchlorate is a sensitizing element for
the propellant in the form of slurry or crosslinked (Fig. 15).
• The shock sensibility behavior (30 kg drop hammer test) of CMCDB or
XLDB propellants is not any different from the other current propellant
families.
Advanced Energetic Binder Propellants
* Slurry
523
Fig. 11.15. Evolution of the friction sensitivity coefficient of XLDB propellants with
70% fillers (slurry and propellant) as a function of fine ammonium perchlorate
content.
• XLDB propellants do not appear to be sensitive to electrostatic discharge
test. But some compositions of CMCDB propellants react to capacitative
discharges. However, the normal reaction of the propellant to this type of
sollicitation is a non-violent combustion (the propellant grain generally
does not present any fragmentation).
• In terms of behavior to thermal stimuli (self-ignition or the cook-off test)
a distinction needs to be made between compositions with or without
ammonium perchlorate. CMCDB and XLDB propellants without
ammonium perchlorate always have critical thermoinitiation tempera-
tures higher than 100°C; these temperatures tend to decrease when the
size of the grain increases. On the other hand, propellants containing
ammonium perchlorate usually exhibit thermoinitiation tempera-
tures below 100°C, but they are not affected by the size of the grain.
Bibliography
1. Steingerger, R. and Dreschsel, P. D., Manufacture of cast double-base propellant.
Advanc. Chem. Serv ., 88, 1-28. 1969.
2. Gordon, S. and Darwell, H. M., Composite modified cast double-base propellants
— technology and application. Technical report, No. 69/5. IMI Summerfield. Paper pre-
sented at the 9th International Aeronautical Congress, Paris, 1969.
3. Helmy, A. M., Investigation of new energetic ingredients for minimum signature propel-
lants. AIAA/SAE/ASME 20th Joint Propulsion Conference, June 1984.
524
Rene Couturier
4. Couturier, R. and Rat, M., Compatibility of ammonium perchlorate with nitrate ester.
ADPA Joint Symposium on compatibility of Plastics and Other materials with explosives,
Propellants and Pyrotechnics. Hilton Head, South Carolina, March 1985.
5. Tavernier, P., Densite gravimetrique et densite de chargement. Memorial des Poudres ,
Tome 31, 197-230, 1949.
6. Rat, M., Longevialle, Y. and Couturier, R., Second order transitions in nitrocellulose
energetic plasticizers systems. Conference on Nitrocellulose Characterization and Double-
Base Propellant Structure. Waltham Abbey, Essex, England, May 1980.
7. Brun, I., Longevialle, Y. and Rat, M., Effect of thermal conditions on the crystallization
kinetics of different nitrate esters, FhG ICT, Jahrestagung, 1989.
8. Hartman, K. O. and Silver, P. A., High performance non-embrittling double-base
propellant. Chemical Propulsion Information Agency Publication No. 340, vol. 1, 1981.
9. Zimmerman, G. A., Kipersky, J. P. Nahoulousky, B. D. and Newey, S. L. Embrittlement
of propellants containing nitrate ester plasticizers, AIAA/SAE/ASME 18th Joint Propulsion
Conference, June 1982.
10. Chi, M. S. and Hartman, K. O., Relationship of polymer structure to mechanical properties
in crosslinked double-base binders. AIAA/SAE/ASME 15th Joint Propulsion Conference,
June 1979.
11. Sumi, K. and Kubota, N., Reduction of plateau-burning effect of HMX based CMDB
propellants. 1 1th International Symposium on Space Technology and Science, Tokyo, 1975.
12. Davenas, A., Amelioration des proprietes balistiques et des proprietes mecaniques tous
temps des propergols sans fumee. AGARD Conference No. 259, Solid Rocket Motors
Technology, 1979.
13. Fifer, R. A., Chemistry of nitrate ester and nitramine propellant. Fundamentals of Solid
Propellant Combustion , Edited by K. K. Kuo and M. Summerfield, Progress in Astronau-
tics and Aeronautics , Vol. 90, 1984.
14. Stack, J. S., Double-base propellants with combustion modifiers, US Patent 3.95 1.704, April
1976.
15. Stack, J. S., Ballistic modifiers, U.S. Patent 3.996.80, December 1976.
16. Sartriana, O. R. and Bracutti, A. J., Ballistic modifiers. US Patent 4.082.584, April 1978.
17. Lengelle, G. and Duterque, J., Combustion des propergols a base d’octogene. AGARD/
PEP Specialists’ Meeting on Smokeless Propellants, Florence, September 1985.
CHAPTER 12
Propellants for Integral Rocket
Ramjet Systems
CHRISTIAN PERUT
1. Introduction
Many countries show an increasing interest in better performance for
tactical missiles, including range improvements, maneuverability and speed.
Solid propellant rocket motor propulsion has proven to be very efficient as
long as the range is modest. When using this technology a significant increase
in the range and the speed can only be obtained at the cost of a considerable
missile weight and volume increase.
In an article published in 1979, R. Marguet, C. Ecary and Ph. Cazin [1]
give the example of a 100 km mission at Mach 2 and low altitude with a
200 kg payload. Solid propellant rocket motor propulsion would result in a 9
to 10 m long missile weighing 5000 kg. However, the use of a kerosene ramjet
would lead to a missile weighing around 1000 kg and 6 m long.
A ramjet engine (shown in Figure 6 in Chapter 1) consists of several major
components. Starting from the front of the missile, they are one or more air
inlets followed by the inlet air diffuser, a fuel supply, fuel metering and
injection devices, a combustion chamber, and a nozzle. In some configura-
tions the fuel supply is located in the combustor. The air is captured by the air
inlet and undergoes compression, resulting in a temperature and pressure
increase, and a decrease in speed. The air is heated in the combustion
chamber by the burning of a fuel whose introduction also triggers a slight
increase in the mass flow rate, of the order of 5-10%. The compressed hot
gases are expanded and accelerated in the nozzle.
Although ramjets are capable of functioning at subsonic flight speeds
greater than Mach 0.8, albeit with poor performance, they are only advanta-
geous at supersonic speeds ranging between Mach 1.5 and Mach 5, and are in
practice used primarily within the Mach 2 to Mach 4 range. Consequently,
the operation of a ramjet requires the missile to reach speeds between Mach
1.5 and 2.5 prior to initiation of ramjet engine operation. The initial solution
525
526
Christian Perut
selected involved the addition of separate, detachable boosters; it was
followed by the use of a solid propellant grain located in the ramjet
combustion chamber. This last configuration, known as the integral rocket
ramjet (Fig. 1), has advantages over the separable rocket booster as it results
in a much more compact missile, and the problems of jettisoning the boosters
after their use are avoided. The chronology of the various stages of operation
of a ramjet with an integral booster is as follows: combustion of the rocket
booster, lasting usually between 3 and 6 s; transition over a period of less than
1 s during which the booster nozzle and the inlet port covers are ejected, the
fuel is injected into the combustion chamber and ignited and, finally, ramjet
operation. The booster may be nozzleless, which avoids the problem of
jettisoning the rocket nozzle (Fig. 2).
The ramjet concept was invented in 1911 by a French scientist, R. Lorin.
The Frenchman R. Leduc applied it to the propulsion of aircraft, and
subsonic flight tests were conducted in 1949. Before and during the Second
World War the Germans studied the application possibilities of the ramjet
concept to missiles and artillery shells. Between the end of the Second World
War and the middle of the 1960s, a large number of countries undertook a
major research effort, which took the shape (in France) of many flight tests of
experimental missiles called CT41, VEGA, R431 and Stataltex; and of
operational developments of ground-to-air or surface-to-air missiles such as
the BOMARC (1957) and the TALOS (1959) in the United States; the
BLOODHOUND (1959) in Great Britain; and the SA4 (1964) in the USSR.
After this period, the research and development effort slackened. Activities
began again around the 1970s with, in particular, the following: introduction
Fig. 12.1. Liquid-fueled integral rocket ramjet.
Propellants for Integral Rocket Ramjet Systems
1 . Boost phase
527
2. Jettisoning of the nozzle
3. Jettisoning of the inlet port covers
in Great Britain in 1975 of the SEA DART; the in-flight evaluation in the US
of the ASALM (advanced strategic air-launched missile) and ALVRJ (ad-
vanced low-volume ramjet) experimental missiles; the development of the
SLAT (supersonic low-altitude target) [2], which could be operational in
1991 [3]; and in France, the flight test of the ANS missile (supersonic anti-
ship) and the operational missile ASMP (medium-range air-to-ground).
The missiles mentioned above are powered with liquid fuel. Another
technical solution consists in feeding the combustion chamber with a hot fuel
plasma through the decomposition of a fuel-rich solid propellant (the amount
528
Christian Perut
Secondary
Fuel rich solid Air inlets combustion chamber
of oxidizer in the propellant is just sufficient to ensure the required ballistic
properties). The fuel-rich grain is placed in a gas generator located upstream
from the combustion chamber of the ramjet. Two configurations are used,
one with a choked gas generator (Fig. 3) where the combustion pressure of
the grain is controlled by one or more nozzles, the other with an unchoked
gas generator where the operation of the gas generator is not separated from
that of the combustion chamber of the ramjet (Fig. 4). The solid-fueled ramjet
engine is referred to as a solid-fueled ducted rocket. In the USSR a ducted
rocket-powered antiaircraft missile, the SA-6, became operational in 1967.
The fuel supply for a liquid-fueled ramjet or for a solid-fueled ducted rocket
is located upstream of the combustion chamber. On the contrary, in the solid-
fuel ramjet concept the fuel is entirely contained in the combustor. The heat
feedback from the combustion zone of the fuel decomposition products with
air determines the fuel grain regression rate. There are two combustor types
[4]. In the non-bypass configuration all of the inlet air passes through the
solid fuel grain (Fig. 5). The combustion efficiency is promoted by a mixing
device located downstream of the fuel grain [4]. In the bypass arrangement a
part of the air is injected downstream of the fuel grain where the combustion
of the fuel-rich products is completed (Fig. 6). In the two cases, the flame is
Fig. 12.4. Ducted rocket with unchoked gas generator.
Propellants for Integral Rocket Ramjet Systems
529
stabilized in the foremost region of the combustion chamber by a recircula-
tion zone created by the inlet step.
Various types of fuel-rich propellant are available. One type is based on
pyrolysis of the binder into a fuel-rich plasma. The pyrolysis is caused by the
reaction of a small amount of oxidizer with a small portion of the binder. A
second type employs a binder and oxidizer in proportions typical of solid
rockets, but also contains a large amount of solid-fuel filler. The rocket
combustion process generates a hot plasma, containing the solid-fuel filler,
and injects it into the secondary combustion chamber where it is mixed with
air and recombusted.
This chapter examines the reasons governing the selection of the major
fuels likely to be used in the composition of a fuel-rich solid propellant, as
well as the main characteristics of typical products belonging to each of the
major families, and makes a survey of integral boosters.
2. Fuel-rich Solid Propellants
2.1. SELECTION OF THE MAIN COMBUSTIBLE COMPONENTS
A fuel-rich propellant for ducted rockets consists of:
• A binder, whose function is to ensure the cohesion of the various
propellant materials, and to supply combustible fuel fragments through
530
Christian Perut
pyrolysis, an oxidizer is employed to react with the binder to produce a
plasma which transports the fuel-rich binder fragments to the secondary
combustion chamber.
• Combustion catalysts.
• Additives, generally used in all propellants, to improve their aging,
processability, including if necessary one or several fuel fillers to increase
energy levels.
An initial selection of the propellant components is feasible on the basis of the
combustion heat values which, due to the mode of operation of a ramrocket,
allow us to assess their energetic quality. The value of components selected in
this manner must later be examined in the light of other selection criteria such
as cost, processability, usability in gas generator, combustion efficiency in
combustor and, if necessary, the signature.
2 . 1. 1. Selection of a binder
Some of the first criteria to be considered when selecting a binder for a fuel-
rich propellant are: the ease of manufacture, and combustion heat values
(Table 1).
Polyesters and polycarbonates contain much more oxygen than polybuta-
diene. Their gravimetric heats of combustion are therefore much lower than
those of the polybutadiene binder, and their much greater density is not
sufficient to compensate for the difference. The classification of these binders,
in a decreasing order of volumetric heating values is as follows:
CTPB = HTPB > polycarbonate > polyester.
The plasticizers generally used with propellants are highly oxygenized; their
incorporation into a polybutadiene binder results in a drop in the combus-
tion heat.
Another parameter which must be taken into consideration is the amount
of fuel-rich solids which can be incorporated into the propellant composition.
From a physical properties perspective, this analysis can be based on the
experience acquired with propellants loaded with ammonium perchlorate
and aluminum. The classification of binders, in a decreasing order of
maximum accessible total solids based on processability and mechanical
properties, is as follows:
plasticized HTPB > HTPB > polyester > polycarbonate.
Polyester and polycarbonate binders, because of their low heating value and
their low loading ratio capability, are therefore not very advantageous. The
respective importance of each of the criteria discussed above depends on the
type of fuel-rich propellant that is considered. In compositions which contain
no combustible solid fuel filler the energy level of the material is provided by
Propellants for Integral Rocket Ramjet Systems
531
rr so
on O ~
o ^ ^ ^
Tt ^
rf <N r-
^ <N Tt
o ^ o
532
Christian Perut
the binder. As we will see later, this type of product contains little oxidizer,
and its manufacture does not require the use of a low-viscosity binder.
Consequently, the choice will often be a non-plasticized polybutadiene
binder.
With compositions containing large percentages of fuel-rich solid particles
the energy is primarily contributed by those particles. A plasticizer should,
therefore, not be automatically excluded if it allows us to significantly
increase the solid loading ratio. Polybutadiene, eventually plasticized, is well
adapted to this type of use.
2. 1.2. Selection of organic energetic additives
Energy can be added to fuel-rich propellants by replacing a portion of the
binder with a solid or liquid hydrocarbonated product. Because polybuta-
diene-type binders contain little oxygen, the increase in gravimetric heating
value likely to be obtained from the substitution of a portion of the binder
with such a compound is very limited. But a substantial increase of the
volumetric heating value can be obtained by using aromatic or aliphatic
cyclical products, which are notably more dense than binders. As for solid
products, the focus has been mainly on aromatic products with densities
appreciably higher than those of the polybutadiene binders [5,6]. The
gravimetric heating value of such products is lower than those of binders, but
because of their much greater density, their volumetric heating value is much
higher (Table 2). The presence of oxygen or nitrogen in the molecule allows
us to significantly increase the density of the product, although not suffi-
ciently to compensate for the loss of gravimetric heating value. The gravi-
metric heating values obtained with liquid products are greater than
those of solid compositions, but the densities are usually lower (Table 3).
These two types of products can be used simultaneously in a fuel-rich
propellant composition.
Table 2 Organic energetic additives (solid products)
Heating value
Product
Density
(g/cm 3 )
Formula
m.p.
(°C)
b.p.
CC)
Gravimetric
(kJ/g)
Volumetric
(kJ/cm 3 )
Anthracene
1.2S
C 14 H 10
217
340
39.9
51.1
Fluorene
1.20
C 13 H 10
116
294
40.2
48.2
Polystyrene
1.05
(C 8 H 8 ) n
—
—
39.9
41.9
Poly (alphamethyl styrene)
1.07
(C 9 H 10 ) n
—
—
40.3
43.1
Anthraquinone
1.44
Ci 4 Hg0 2
286
380
31.4
45.2
Naphthylamine
1.12
c 10 h 7 nh 2
50
301
36.9
41.3
Dicyandiamide
1.40
c 2 n 4 h 4
210
d
18.6
26.0
Propellants for Integral Rocket Ramjet Systems
Table 3 Organic energetic additives ( liquid products )
533
Atomic composition
Heating value
Density
(g/cm 3 )
7 0 (mass;
Gravimetric
(kJ/g)
Volumetric
(kJ/cm 3 )
Product
C H
o
Hydrogenated terphenyl
1.006
90.8 9.2
0
42.6
42.9
Hydrogenated
polycyclopentadiene resin
1.053
89.6 10.4
0
44.3
46.6
Poly(styrene-indene)
1.051
91 7.6
1.4
41.0
43.1
Hydrogenated dimer of
norbornadiene
1.08
90.2 9.8
43.7
47.2
2 . 1.3. Selection of inorganic fuel fillers
The interest has generally focused on carbon, zirconium, aluminum,
magnesium, and boron [6,7]. Boron carbide and titanium are sometimes also
mentioned (Table 4).
Although its combustion heat is high, beryllium is excluded, as for all
propellants, because of the toxic properties of its oxide as a combustion
product.
The order of classification of these products, as a function of their
gravimetric heating value, is:
B > B 4 C > C > A1 > Mg > Ti > Zr
In most cases the performance per unit of volume is the important factor
which is sought after. Making a distinction between amorphous carbon black
and graphite, the classification is as follows:
B > B 4 C > Ti > A1 > Zr > C (graphite) > C (carbon black) > Mg
Table 4 Inorganic fuel fillers
Heating value
Product
Density
(g/cm 3 )
Gravimetric
(kJ/g)
Volumetric
(kJ/cm 3 )
Beryllium
1.84
66.5
122.5
Aluminum
2.70
31.1
83.9
Boron (amorphous)
2.22
59.3
131.6
Graphite
2.25
32.8
73.8
Carbon black
1.63
32.8
53.3
Magnesium
1.74
24.7
43.0
Zirconium
6.49
12.0
78.2
Titanium
4.5
19.7
88.8
Boron carbide
2.52
51.5
129.8
534 Christian Perut
Due to their high density, titanium and zirconium now attract more
interest.
However, we must point out that for an equal volumetric performance it is
preferable to have the highest possible gravimetric energy. This is due to the
fact that an increase of the density implies a greater weight for the fuel-rich
grain, with the detrimental result of a heavier propulsion system, because of
the increase in weight of the gas generator and of the booster, which needs to
be more powerful.
A preliminary assessment of the increase in performance that might be
obtained by switching from a composition without particles to a particle-
laden composition can be made by comparing relative heating values. When
taking the gravimetric heating value into consideration, only boron and
boron carbide have combustion heats greater than that of a polybutadiene-
type binder. But because of their greater density, all of these fillers have
volumetric heating value that are greater than those of the binder.
2. 1.4. Theoretical energetic performances
The following thermodynamic calculations for various filled and unfilled
compositions are provided to demonstrate their relative energy merits. These
examples involve one hydrocarbon-fueled composition and compositions
with polybutadiene binder with 25 % ammonium perchlorate and 50 % of one
of the most common energetic fillers quoted in the field, i.e. aluminum,
magnesium, carbon, zirconium or boron. These amounts were selected
arbitrarily, and do not take into account either the manufacturing problems
specific to each of these additives, or the amount of ingredients that must be
selected to ensure the functional properties required from the gas-generating
grain.
Before an assessment of the theoretical performances of these fuel-rich
propellants can take place, we need to establish standard conditions for the
operation of the ramjet. For this chapter we have selected a chamber pressure
equal to 0.57 MPa, the enthalpy of formation attributed to air
corresponding to a flight at Mach 2 and sea level. In addition, the calcula-
tions are done on the basis of different proportions of air and fuel. These
proportions are expressed in terms of the value of the equivalence ratio, a
term that stands for the quotient of the ratio of the mass flow rate of fuel and
air versus the same ratio for a stoichiometric mixture (see Chapter 3).
The evolutions of the specific impulse (7 S ) and of the volumetric specific
impulse (I s p) as a function of the equivalence ratio are illustrated in Figs 7
and 8. The specific impulse is the ratio of the thrust to the product of the
acceleration due to gravity and the mass flow rate of the fuel-rich propellant.
For a low equivalence ratio the classification of the combustible solids in a
decreasing order of specific impulse is as follows:
B > C > A1 > Mg > Zr
Propellants for Integral Rocket Ramjet Systems
535
0.5 1 1.5 2
<P
Fig. 12.7. Theoretical performances of fuel-rich propellants (M = 2; Z = 0;
P = 0.57 MPa).
This ranking order is identical to that established on the basis of the
combustion heat.
Based on the volumetric specific impulse, which is the criterion for the
selection when the volume available for the gas generator is limited, the
classification is as follows:
B > C (graphite) > A1 > Zr > Mg
The relative values of a composition without particles are shown on the same
diagram, to serve as a reference.
2.2. SELECTION OF A COMPOSITION TYPE
The criteria for selecting the type of composition must take features of
future missions other than theoretical energy into consideration.
The combustion in the chamber of the ramjet of the decomposition
products from hydrocarbon-fueled compositions and carbon compositions
leads exclusively to the production of gaseous products, provided that high
levels of combustion efficiency are obtained. Therefore, these compositions
produce low levels of exhaust smoke.
The oxides from aluminum, zirconium, magnesium and boron, on the
other hand, are solid at ambient temperature. Therefore, these fuel-rich
propellants produce high levels of exhaust smoke.
Based on their energy and exhaust smoke levels, fuel-rich propellants can
be classified into three categories: metal-loaded compositions with high
536
Christian Perut
0.5 1 1.5 2
Fig. 12.8. Theoretical performances of fuel-rich propellants (M = 2 ; Z = 0;
P = 0.57 MPa).
smoke levels, carbon compositions and hydrocarbon-fueled compositions
with low smoke level.
The hydrocarbon-fueled compositions generate lower molecular weight
hydrocarbon fragments which are burnt later in the secondary combustion
chamber. Consequently, these compositions exhibit characteristics of com-
bustion similar to gaseous hydrocarbons.
2.2. 1. Compositions with a high content of metal
Four metals offer the desired properties: boron, aluminum, zirconium and
magnesium.
The thermodynamic computations demonstrate that boron fuel-rich pro-
pellants are potentially highly energetic. However, the expected energy is only
likely to be produced if the boron particles ignite and burn in the air within a
very short period of time, compatible with the residence time in the
combustion chamber, usually less than 5 ms. It is also difficult to burn at low
pressures. For these reasons, boron combustion has been the object of very
extensive research [8,9].
Boron particles are naturally coated with a layer of boric oxide, which has
a very high boiling temperature (2133 K) that interferes with the combustion.
A. Macek’s research [8] revealed that boron particle combustion occurs in
two successive phases. First, the particle ignites, followed by an extinction
phase during which no luminous phenomenon is observed that would
Propellants for Integral Rocket Ramjet Systems 537
correspond to the end of the evaporation process of the oxide layer, and then
to the end of combustion [8,9]. The ignition temperature, defined as the
minimal temperature necessary for combustion, is virtually independent of
the size of the particle in the case of products with a small particle size. This
temperature is 1980 K for a particle measuring 1 /im and 1920 to 1930 K for a
particle of 30-40 /im under conditions of a dry atmosphere, and under a
pressure of 1 atm and an oxygen molar fraction of 0.2 [9]. With large
particles, the burn time varies as the square of the diameter, and it is virtually
independent of the pressure, thereby indicating that kinetic behavior is
limited to the diffusion phenomena. With fine particles the burn time is
proportional to the diameter, and in this case the burning rate is limited by
the chemical kinetics and depends on the pressure. There are variations in
behavior for diameters of a few tens of microns [9].
The burn time in a gaseous mixture with 20% oxygen and 80% nitrogen at
2240 K is approximately 0.6 ms for particles measuring 1 /im and 1.5 ms for
particles measuring 3 /im [9]. Because of the very short residence time in the
combustion chamber, these results show that very fine particles must be used.
The products usually selected have particle diameters smaller than 3 /im.
Various solutions may be considered to promote the combustion of the
boron inside the combustion chamber of a ramjet, such as increase of the
temperature, chemical modification of the boron, or optimization of the
architecture of the combustion chamber; this last point is discussed in the
following section.
The incorporation of a small quantity of metal into the composition may
promote the combustion efficiency. The additive is supposed to react rapidly
in the zone where the air and the combustible products mix, and cause an
increase of the temperature [9].
Some research has demonstrated the advantage of coating the boron
particles with lithium fluoride to facilitate their ignition. The mechanism
involved is based on the formation of a compound with a boiling temperature
that is lower than that of the boron oxide [9].
Fuel-rich propellants with a high content of aluminum cannot be used
because of their significant tendency to obstruct the nozzles or the dia-
phragms of the gas generators.
Thermodynamic computations show that, for an identical solid loading
ratio, magnesium compositions have a specific impulse greater than those of
zirconium compositions. Due to the fact that zirconium is much more dense
than magnesium, this result is inverted when the volumetric specific impulse
is considered. Consequently, a comparison between these two types of
compositions is only feasible after a final assessment of their applications has
been done. In general, magnesium compositions have proven to be more
advantageous than zirconium compositions.
Finally, magnesium is introduced in a gaseous state into the combustion
chamber because of the very high flame temperature of magnesium composi-
538
Christian Perut
tions, ranging from 1950 to 2400 K, compared to the boiling temperature of
magnesium, 1380 K. The combustion of the magnesium in the combustion
chamber is therefore very rapid.
2 . 2 . 2 . Carbon compositions
The burning rate of carbon particles is governed either by the kinetic of the
oxygen diffusion, or by the speed of the superficial reaction if one of these two
processes is much more rapid than the other; otherwise it is governed by
both. The nature of the phenomenon that limits the burning rate depends on
the temperature and the particle size.
Major studies reported in the literature demonstrate that it is necessary to
use very fine particles, for which the burning rate is probably controlled by
the chemical kinetic, and consequently that the nature of the carbon used is a
very important parameter in obtaining satisfactory combustion efficiency
[11-13].
2.3. THEORETICAL ENERGETIC PERFORMANCES
The performance analyses discussed above were intended to compare the
advantage of various fuels, without taking into account any of the other
characteristics, in particular the processability characteristics. Figure 9 shows
Type of composition
V/A Boron
0.5 1 1.5 2
*P
Fig. 12.9. Theoretical performances of fuel-rich propellants (M = 2; Z = 0;
P = 0.57 MPa).
Propellants for Integral Rocket Ramjet Systems
539
the energetic performances of feasible compositions on a graph plotting
[volumetric specific impulse] versus [equivalence ratio]. It illustrates the
potential advantage of boron compositions which present, for an equivalence
ratio of 0.4, a volumetric specific impulse 30-45% greater than the best
hydrocarbon-fueled composition included in the figure; and carbon composi-
tions which, together with a low visual signature, have a volumetric specific
impulse 12-20% greater than that of the best hydrocarbon-fueled composi-
tion. We should add that, within the carbon compositions, we have included
carbon black and graphite formulations that are not identical from the point
of view of combustion in the chamber of a ramjet. Additionally, hydrocar-
bon-fueled compositions can be enhanced by the addition of a small amount
of metal, carbon or boron.
2.4. MAJOR PROPERTIES OF SEVERAL FUEL-RICH
PROPELLANTS
The selection of a fuel-rich propellant is based on various criteria:
• theoretical performances,
• processability,
• mechanical properties,
• safety properties,
• ballistic properties,
• control,
• combustion efficiency,
• signature,
• cost.
Special mention should be made of the capability of modulating the flow rate
[14]: it allows us to adjust the combustible flow to the flow of air collected,
which varies according to the altitude and the velocity of the missile, in order
to remain within a specific range of equivalence ratio. The specification of the
ratio of modulation is therefore imposed by the expected flight envelope,
speed, and altitude. The more extensive the flight, velocity and altitude
envelope, the higher the modulation ratio will have to be. For the trajectory
of an air-to-air missile, launched at low altitude, then cruising at high
altitude, the range may be increased by over 300 % by using a ramrocket with
a throttleable gas generator [15].
In the case of the choked gas generator, the modulation of the fuel rate is
done by a valve. The modulation ratio can be defined as the ratio of the
burning rate at maximum operating pressure for the minimum temperature
likely to be encountered by the fuel-rich propellant, versus the burning rate at
the minimum operating pressure at the maximum temperature. It is therefore
dependent on the pressure exponent (which cannot exceed the value of 0.75
by much for reasons of stability), on the temperature sensitivity coefficient,
540
Christian Perut
and on the operating pressure range, whose highest value is limited by the
mechanical strength of the case, and whose lowest value is limited by the
stable operation pressure limit of the gas generator, and by the pressure
existing in the combustor. The architecture of the valve and the materials it is
made of, must be tailored to the particular fuel-rich propellant used, to ensure
the valve’s resistance to the temperature of the effluents and to prevent
obstructions caused by deposits or particles.
The pressure inside an unchoked gas generator is not disassociated from
the pressure of the combustor. This means that the grain burns at a pressure
directly related to the flight conditions. It is therefore “sufficient” when the
fuel-rich propellant has the required ballistic properties to have the fuel flow
rate self-adjust to that of the air.
For purposes of illustration, the following sections describe the main
properties of a smokeless hydrocarbon-fueled composition, and a boron
composition tailored to the operation of a choked gas generator.
2.4. 1. Hydrocarbon-fueled composition for a
choked gas generator
The major components of hydrocarbon-fueled compositions are a binder,
an oxidizer, and sometimes a hydrocarbon filler.
With a given binder, the theoretical performances depend mostly on the
nature and the amount of oxidizer. Figure 10 illustrates, in a polybutadiene
binder composition, the evolution of the specific impulse and of the volu-
metric specific impulse versus the amount of ammonium perchlorate.
The energetic performances decrease as a function of the oxidizer content;
the maximum values correspond to the pure binder.
The combustion of compositions with very low oxidizer content is charac-
terized by the presence after firing of a compact combustion residue in the gas
generator. For compositions with an ammonium perchlorate content ratio
ranging from 25 to 30%, the amount of residue in relation to the initial total
weight of the grain is usually between 5 and 15%, depending on the
formulation of the fuel-rich propellant. The presence of this residue causes
first, a drop in the volumetric specific impulse, mostly due to the decrease of
the effective weight of fuel loaded on the gas generator for a given volume.
More importantly, the presence of the residue runs the risk of affecting the
operational reliability of the gas generator, by obstructing the ejection
orifices with fragments breaking away from the main body of the residue.
For these reasons the compositions usually selected today contain an
oxidizer amount sufficient to prevent the formation of abundant residue.
The formulation of a hydrocarbon-fueled composition follows various
specifications concerning energy level and modulation capabilities. Accord-
Propellants for Integral Rocket Ramjet Systems
541
Fig. 12.10. Hydrocarbon fueled compositions influence of the amount of ammonium
perchlorate on the theoretical performance (M = 2; Z = 0; P = 0.57 MPa; $ = 0.4).
ing to the type of mission involved and the resulting specifications, the focus
is placed on this or that characteristic.
T. D. Myers gives the example of a fuel-rich propellant with extensive
modulation capabilities exhibiting a mass flow rate ratio of 1 to 18, for a
pressure exponent of 0.55 and a minimum operating pressure of 0.14 MPa
[15].
The characteristics described below are those of a hydrocarbon-fueled
composition. This composition, which does not contain metal and ammon-
ium perchlorate, is smokeless, but has a low modulation capability. Its basic
formula is (1000 g base):
^47.31 ^50. 19 N 8i2 7 0 1 6.58
It consists mainly of a polybutadiene binder and an organic oxidizer. Its
measured combustion heat is 33 KJ/cm 3 .
2.4. 1. 1. Theoretical performance
The temperature inside the gas generator is 1350 K.
The thermodynamic computations for the chamber of the ramjet were
made by considering an operational pressure of 0.57 MPa and simulating
flight conditions of sea level and Mach number 2.
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Christian Perut
00
a.
(S)
i l I U
0.5 1 1.5 2
Fig. 12.11. Hydrocarbon fueled composition theoretical performances (M = 2; Z =
0; P = 0.57 MPa).
Figure 1 1 shows the evolution of the density-specific impulse (I s p) versus
the equivalence ratio (<£).
Figure 12 illustrates the evolution of the temperature as a function of the
equivalence ratio. Its maximum value is of the order of 2590 K in an
equivalence ratio ranging from 1.1 to 1.35. The stoichiometric fuel-air ratio
is 0.143.
2.4. 1 .2. Processability
Because of its low total solids this composition is very easy to manufacture.
The viscosity of the slurry at casting is 2300 poises. Pot-life is excellent: the
viscosity is 4400 poises for 12 h after casting.
Consequently, the casting of fuel-rich propellant is very easy, even in the
case of grains with very complex shapes. Gravity alone is sufficient to fill the
molds, without having recourse to any devices.
2.4. 1.3. Mechanical properties
This composition has excellent mechanical properties, also due to its low
filler loading ratio. At 20°C, and with a cross head rate of 50mm/min,
maximum stress is 0.8 MPa, the elastic strain 52%, and the strain at
maximum stress 120%.
Propellants for Integral Rocket Ramjet Systems
543
Fig. 12.12. Hydrocarbon fueled composition theoretical combustion temperature in
air.
2.4. 1.4. Safety properties
Table 5 lists the sensitivity characteristics in accordance with the opera-
tional modes described in Chapter 7.
2.4. 1.5. Ballistic properties
The burning rate at 5 MPa is 3.8 mm/s. The pressure exponent is 0.45,
providing a mass flow rate ratio of 3.8 at 20°C between 0.7 and 15 MPa. The
evolution of the pressure curve versus time indicates low-amplitude pressure
fluctuations at low pressure.
The modulation ratio between — 40°C and 60°C is 3 (Fig. 13).
Table 5 Hydrocarbon fueled composition : safety properties
Tests
Results
Impact sensitivity
Height of non-propagation of violent reaction
> 4 m
(30 kg fall-hammer)
Height of non-reaction to impact
2 m
Sensitivity to friction
Coefficient of sensitivity to friction
0% at 353 N
(Julius Peters)
Cook-off
Critical temperature
220°C
Card gap test
Number of cards
110
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Christian Perut
I L
Fig. 12.13. Hydrocarbon fueled composition ballistic properties.
2.4. 1.6. Combustion efficiency
The composition has been evaluated in a combustor with 200 mm dia-
meter and four lateral air intakes, simulating a flight speed of Mach 2
and an altitude of 1.5 km.
The gas-generating grain operates at an average pressure of 3.2 MPa and
releases 0.250 kg/s for 47 s. The equivalence ratio is 0.38. The combustion
efficiency, which is defined as the ratio between the burned gas mass flow rate
and the injected gas mass flow rate, is 0.91.
2.4. 7.7. Signature
This composition, which does not contain metal and ammonium per-
chlorate, is smokeless.
Propellants for Integral Rocket Ramjet Systems 545
2.4.2 . Boron composition
Boron composition consists mostly of a binder, ammonium perchlorate,
fine boron and sometimes one of several additives designed to facilitate the
combustion of the boron.
The boron composition, described here, was selected on the basis of its
processability, its mechanical properties, and its operational characteristics in
a gas generator. It does not correspond to the higher energetic performances
that may be obtained with this type of formulation. It is designed to operate
in a choked gas generator.
2 . 4 . 2 . 1. Theoretical performances
The theoretical performance of these compositions depends greatly on the
amount of boron. For a 25% content of ammonium perchlorate, the
volumetric specific impulse changes, according to our standard calculations
(P = 0.57 MPa, M = 2, Z = 0, (j> = 0.4), from 1778 to 2028 sg/cm 3 (i.e. a 14%
increase), when the amount of boron increases from 40 to 50%.
Figures 14 and 15 show respectively the evolution of the volumetric specific
impulse and the combustion temperature versus the equivalence ratio for the
above composition. The peak temperature is at an equivalence ratio of 1.15.
2000
1500
1000
500
i i 1 1
0.5 1 1.5 2
Fig. 12.14. Boron composition theoretical performances (M = 2; Z = 0;
P = 0.57 MPa).
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Christian Perut
3000
2500
*
2000
o 1 1 1 1 1
0.5 1 1.5 2
M
Fig. 12.15. Boron composition theoretical combustion temperature in air.
The temperatures obtained are much higher than with hydrocarbon-fueled
compositions.
2. 4.2.2. Processability
The manufacture of boron compositions with good mechanical properties
is made somewhat difficult by the chemical reactions between impurities
usually coating boron and the constituents of the binder, requiring a
definition of the specification for the raw material, and the creation of a
specially designed method for the mixing operation. Once this has been done,
the manufacturing qualities and the mechanical properties are highly satisfac-
tory. The viscosity of the slurries at casting is between 10000 and 15000
poises. The manufactured grains are end-burning. They are manufactured
using the casting and gravity process.
2. 4. 2. 3. Mechanical properties
In terms of the mechanical properties for the binder, the maximum stress
is between 1.8 and 2.4 MPa, and the strain at maximum stress is between 37
and 44%.
2. 4. 2. 4. Safety properties
These properties are shown in Table 6.
Propellants for Integral Rocket Ramjet Systems 547
Table 6 Boron composition: safety properties
Tests
Results
Impact sensitivity
Height of non-propagation of violent reaction
> 4 m
(30 kg fall-hammer)
Height of non-reaction to impact
2.5 m
Sensitivity to friction
(Julius Peters)
Coefficient of sensitivity to friction
0% at 253 N
Cook-ofT
Critical temperature
187°C
Card gap test
Number of cards
< 1
2.4. 2.5. Ballistic properties
The compositions shown in Fig. 16 burn at a pressure of 5 MPa between 10
and 15mm/s. They produce no combustion residue, but leave in the gas
generator slag with a mass corresponding to less than 1 % of the initial mass
of the grain. The compositions discussed here have low-pressure exponents,
smaller than 0.1 when the pressure exceeds 3 MPa.
Because the boron compositions are heavily particle-laden they show a
high propensity to create obstructions in the nozzle, resulting in pressure
evolution curves versus time that are progressive. Two factors have influence
_i i i i i i i i i i —
1 2 3 45678910
P(MPa)
Fig. 12.16. Boron composition ballistic properties (end burning grain— 90 or
117 mm diameter).
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Christian Perut
Fig. 12.17. Boron composition static test-end burning grain (177 mm diameter;
300 mm length).
on this phenomenon: one is the internal architecture of the gas generator, and
the other is the formulation of the fuel- rich propellant. Figure 17 shows the
recording of a firing corresponding to an optimal configuration.
2. 4.2.6. Combustion efficiency
For reasons briefly discussed in the preceding section, obtaining high
combustion efficiency in a combustor is difficult, and requires a careful
organization of the flows inside the combustion chamber.
The research done by K. Schadow [16,17] and S. W. Abbott, L. D. Smoot
and K. Schadow [18] demonstrated that because the temperature in the gas
generator is generally lower than the 1950 K ignition temperature of boron,
good combustion efficiency can be attained only when the gas generated by
the composition burn with the air at sufficiently high equivalence ratio levels
to produce a temperature high enough to guarantee that the heated boron
particles will be able to ignite. They have also demonstrated that combustion
efficiency drops when the pressure of the combustor decreases.
C. Vigot, L. Bardelle and L. Nadaud [10] have studied the combustion of a
fuel-rich propellant with 35% boron. They demonstrated that the combus-
tion efficiency can be improved by injecting the fuel at the forward end with
converging jets, and by introducing only a portion of the air close to the
forward end. This arrangement creates an area where the temperature
Propellants for Integral Rocket Ramjet Systems 549
attained is sufficiently high to guarantee the ignition of the boron, since the
ratio of the fuel-air mixture is close to the stoichiometry. The remainder of
the air is injected downstream. It is important that the distance separating
these two injection planes not exceed a certain specific value. This value
depends on many factors such as the geometry of the air intake connections
in the combustion chamber, and the distribution of the velocity of the air.
2.4.2. 7. Signature
Because the boron compositions are heavily particle-laden, they are
smoky.
3. Boosters for Integral Rocket Ramjets
Ramjets and ducted rockets are accelerated to or above the minimum
required takeover speed by a solid propellant booster [19-22]. Three basic
configurations are generally described: externally mounted boosters, whether
permanent or droppable, tandem rocket ramjet and integral rocket ramjet.
The integral rocket ramjet concept permits the overall missile dimensions to
be minimized and so has significant drag, weight and volume advantages
when compared to the two other configurations. There are also disadvan-
tages to the integral concept. Specifically, the booster and the combustor
share a common chamber. This requires that additional design emphasis be
placed on the propellant booster grain, the ramburner thermal protection
and the bonding of the grain to the thermal insulator.
The booster operating pressure is between 7 and 14 MPa and the ramjet
operates under 1 MPa. The case is fabricated to withstand the high booster
pressure and the thermal protection must resist the case mechanical deforma-
tion induced during the booster phase. The booster requires a smaller nozzle
throat area than the ramjet due to the order of magnitude difference between
the ramjet and the booster operating pressures. Two configurations can be
used: ejectable nozzle system and nozzleless booster.
The booster is sized to accelerate the missile from ground or air launch
speed to a velocity at which ramjet thrust exceeds drag by some margin. The
Mach number for ramjet takeover is generally between 1.5 and 2.5.
For a given diameter, this requirement dictates a minimum grain length.
Generally, this length exceeds the value required to reach the required ramjet
combustion efficiency. This is true even for missiles launched from aircraft.
One notable exception is the boron propellant ducted rocket. For a given
ramjet configuration, greater booster length results in a shorter fuel tank and
therefore a shorter range. According to Myers [19], a 1% increase in
propellant grain length could result in a 5-10% loss in vehicle range. Thus a
high volumetric specific impulse propellant and a high volumetric ratio grain
are important requirements.
550
Christian Perut
It is necessary to restrict drag losses during the booster phase. Consequent-
ly, the grain operating time is minimized within the limits dictated by the
maximum acceleration allowed by the missile. The grain burn time is
generally between 3 and 6 s. Therefore, medium-to-high burning rate propel-
lants are required for boosters.
The thermal protection of the case must withstand heat during the booster
and the ramjet phases. During the booster phase the combustion gases are
reduced and are produced at temperatures up to 3600 K and pressures up to
14 MPa, but gas velocities and operating times are short. In the ramjet the
temperature and the pressure are much lower, but the gases are oxidizer-rich
and velocities can reach 300 to 340 m/s with operating times between several
tens and several hundred seconds. In order to reduce inert weight and
volume, thermal protection thickness is limited.
The different thermal protection concepts are discussed in Chapter 13.
During the transition phase the rocket motor transforms itself to a ramjet
combustor (Figure 2). The vehicle drag forces are high and the missile quickly
slows down. According to Myers [19] typically slowing down is about 0.1
Mach number per second. Therefore, transition must be done swiftly. Energy
is released after booster operation by the combustion of propellant grain
slivers, part of liner and decomposition products resulting from booster
heating. The fuel injection and its ignition must be timed so that the total
energy released does not cause excessive combustor pressure increase which
would result in inlet unstart. Shortening the transition phase requires that
careful attention be focused on residual booster materials and the careful
shaping of booster burning profiles at the end of operation. Consequently, the
transition phase dictates new requirements for the booster grain:
• Sliverless grain, although grain slivers always exist to some extent, caused
primarily by dimensional tolerance variations during manufacture.
• Minimum liner thickness. One technical answer to direct bonding is
described in Chapter 13.
The nozzleless booster represents an alternative concept to the ejectable
nozzle system [23,24]. The advantages of this design are indicated in Chapter
2. This configuration places additional requirements by comparison with the
nozzled motor design:
• the burning rate must be higher,
• the stress capacity at the high operating temperature must be raised to
avoid grain damage under the shear loads caused by the pressure
difference between the head-end and the aft-end,
• small pressure exponent — lowering the pressure exponent permits a
significant performance increase. According to Procinsky and McHale
[23], lowering the pressure exponent from 0.48 to 0.28 induces a 3.0%
increase in total impulse.
Propellants for Integral Rocket Ramjet Systems
551
The booster propellants are generally of the high-energy aluminized compo-
site type as low visual signature is not required (Chapter 10). The formula-
tions are optimized to achieve the mechanical properties suitable for a case-
bonded grain. They include a liquid or a solid burn rate catalyst to achieve
the required burning rate (between 20 and 35 mm/s at 7 MPa). An alternative
propellant composition is one which employs zirconium. The interest in
zirconium is due to its high density (6.49). Typical compositions include an
HTPB binder, ammonium perchlorate and high loading of zirconium (up to
45%). Typical zirconium propellants possess lower specific impulse, higher
density and higher volumetric specific impulse than typical aluminized
formulations.
Aluminum and zirconium compositions show some ballistic property
differences. The specific impulse efficiency losses for zirconium-loaded com-
positions are more important than those for aluminum compositions. Also
zirconium propellants show greater sensitivity to motor scaling effects [25].
Nevertheless, the substitution of an aluminum composition by zirconium
formulation in a given configuration grain would induce a shorter but heavier
booster [23]. Another disadvantage of zirconium composition is the relative-
ly high cost of zirconium.
Bibliography
1. Marguet, R., Ecary, C. and Cazin, P., Studies and tests of rocket ramjets for missile
propulsion, 4th International Symposium on Airbreathing Engines, Orlando, AIAA paper
no. 79.7037, 1979.
2. Wanstall, B., Statofusees pour Longs Parcours a Vitesse Supersonique, Interavia, 12,
1331 1334, 1984.
3. Wanstall, B., Slat the Mach 3 Target to Test Ship’s Defences, Interavia Aerospace Review ,
44,(3), 242, 1989.
4. Myers, T. D., Special problems of ramjet with solid fuel, ramjet and ramrocket propulsion
systems for missiles. AGARD Lecture Series no. 136, pp. 6. 1-6.9, 1984.
5. Besser, H. L., Solid propellant ramrockets, ramjet and ramrocket propulsion systems for
missiles. AGARD Lecture Series no. 136, pp. 7.1-7.30, 1984.
6. Cohen, N. S., Combustion considerations in fuel-rich solid and hybrid propellant systems in
airbreathing propulsion. AIAA 6th Aerospace Sciences Meeting, New York, AIAA Paper,
no. 68-96, 1968.
7. McClendon, S. E., Miller, W. H. and Harty, C. M., Fuel selection criteria for ducted
rocket application. AIAA paper, no. 80-1120, 1980.
8. Macek, A. and McKenzie Semple, J., Combustion of boron particles at atmospheric
pressure, AIAA 5th Propulsion Joint Specialist Conference US Air Force Academy,
Colorado, AIAA paper no. 69-562, 1969.
9. King, M. K., Ignition and combustion of boron particles and clouds. Journal of Spacecraft ,
19(4), 294-306, 1982.
10. Vigot, C., Bardelle, L. and Nadaud, L., Improvement of boron combustion in a solid-fuel
ramrocket. AIAA/ASME/SAE/ASEE, 22nd Joint Propulsion Conference, Huntsville, AIAA
paper no. 86-1590, 1986.
11. Szekely Jr, G. A. and Faeth, G. M., Combustion properties of carbon slurry drops. AIAA
Journal. , 20(3), 422-429, 1982.
12. Ubhayakar, S. K. and Williams, F. A. Burning and extinction of a laser-ignited carbon
particle in quiescent mixtures of oxygen and nitrogen, J. Electrochem. Soc. Solid-State
Science Technol., 123(5) 747-756, 1976.
552
Christian Perut
13. Smith, I. W., The intrinsic reactivity of carbons to oxygen, Fuel , 57, 409-414, 1978.
14. Thomaier, D., Speed control of a missile with throttleable ducted rocket propulsion. 44th
Symposium in Air-Launched Weapons, Guidance and Control, AGARD Conference
Proceedings 431, pp 24.1-24.15, 1987.
15. Myers, T. D., Moteurs a Statoreac tews/ Fusee a Combustibles Solides. Armada Internation-
al, no. 3, pp. 122-125, 1984.
16. Schadow, K., Boron combustion characteristics in ducted rockets. Combustion Science and
Technology, 5, 107-117, 1972.
17. Schadow, K., Study of gas-phase reactions in particle-laden, ducted flows, AIAA Journal ,
11(7), 1042-1044, 1973.
18. Abbott, S. W., Smoot, L. D. and Schadow, K., Direct mixing and combustion efficiency
measurements in ducted, particle-laden jets. AIAA Journal , 12(3), 275-282, 1974.
19. Myers, T. D., Integral boost, heat protection, port covers and transition, ramjet and
ramrocket propulsion systems for missiles. AGARD Lecture Series no. 136, pp. 4.1-4.20,
1984.
20. Webster, F. F., Liquid fueled integral rocket ramjet technology. AIAA/SAE 14th Joint
Propulsion Conference, Las Vegas, AIAA paper no. 78-1108, 1978.
21. Butts, P. G. and Myers, T. D., Integral booster motor interface requirements. AIAA/SAE
14th Joint Propulsion Conference, Las Vegas, AIAA Paper 78-1060, 1978.
22. Marguet, R. and Cazin, Ph., Ramjet research in France: realities and perspectives. 7th
International Symposium on Air Breathing Engines, Beijing, 1985.
23. Procinsky, I. M. and McHale, C. A., Nozzleless booster for integral-rocket-ramjet missile
systems. Journal of Spacecraft , 18(3), 193 199, 1981.
24. Nahon, S., Nozzleless solid propellant rocket motors: experimental and theoretical investi-
gations. AIAA/SAE/ASME 20th Joint Propulsion Conference, Cincinnati, AIAA Paper no.
84-1312, 1984.
25. Coughlin, J. P., Impulse efficiency correlations for aluminum and zirconium propellants,
AIAA/SAE/ASME, 17th Joint Propulsion Conference, Colorado Springs, AIAA paper no.
81-1381, 1981.
CHAPTER 13
Thermal Insulations, Liners
and Inhibitors
JEAN-MICHELTAUZIA
1. Inhibiting Materials and Thermal Insulation in
Solid Propulsion
The function of a rocket motor is to deliver a thrust according to a
predetermined program.
With solid propellant rocket motors, theory allows us to relate the thrust
law required by the designer to the evolution versus time of the burning
propellant surface [1,2].
The evolution of that surface depends heavily on the presence of organic
materials adhering strongly to the propellant. These materials, called com-
bustion inhibitors, limit the initial combustion surface so that the combina-
tion of the grain geometry and the combustion law of the propellant results at
any instant in the desired thrust.
To completely fulfill their role the inhibitors must present a whole set of
characteristics which will be described in detail later in this chapter. The most
important is an excellent bonding to the propellant. This property is essential
for the reliability of the rocket motor, because any debonding between the
inhibitor and the propellant results almost invariably in a failure of the rocket
motor due to an uncontrolled pressure rise.
Other inert materials are often present in the combustion chamber,
ensuring such functions as the bonding of the propellant with the wall of the
motor case (liner), or the thermal insulation of case surfaces exposed to the
hot gases (thermal protection).
In the following pages we will use the term “insulating materials” for these
various materials (inhibitors, restrictors, liners, thermal protections) illus-
trated at figure 1.
Very strong interactions take place between the design of the grain, the
propellant and the various insulating materials. Consequently, the properties
of the latter have a significant influence on performance, service life and cost
of rocket motors.
553
554
Jean-Michel Tauzia
Case Thermal protection Propellant grain Lateral grain
X
Mechanical device
holding the grain
Free-standing grain
Thermal protection bonded to the case H ner
Clearance
Case bonded grain
Case
inhibitor
Frontal grain
inhibitor
Stress relief device
Fig. 13.1. Configuration of a solid propellant rocket motor (without nozzle).
2. Background
2.1. SPECIFICATIONS OF INSULATING MATERIALS
The insulating materials must satisfy many specifications difficult to
quantify. They include, but are not limited to:
• Sufficient bonding within the entire range of working temperatures of the
motor.
• Low ablation rate, to minimize the inert mass on board. At the same time
the resulting “char” must remain porous: the decomposition gases must
exhibit a low molecular mass, the pyrolysis of the material must not lead
to emission of smoke or flashes.
• Low thermal conductivity.
• High specific heat.
• Low density.
• Mechanical strength compatible at all temperatures with the deformation
of the grain during the various manufacturing and storage phases, or with
those deformations resulting from various thermal and mechanical stress
to which the rocket motor is subjected in the course of its life including, of
course, firing.
• Pyrotechnic compatibility with the live constituents of the motor (propel-
lant, ignition powder).
• Sufficient electric conductivity to avoid electric charge build-up.
• Chemical compatibility with the components of the motor: the insulating
materials must not upset the chemistry of propellant but maintain the
nominal characteristics of the latter.
• Good gas permeability.
Thermal Insulations. Liners and Inhibitors
555
• Low humidity absorption.
• Good aging characteristics.
2.2. THEORETICAL DATA REQUIRED FOR THE DESIGN OF
INSULATING MATERIALS
The development of insulating materials for rocket motors calls for deep
knowledge in multiple fields of studies, such as chemistry, thermodynamics,
mechanics, optics and many other branches of physics.
Because of their particular importance for the work of the rocket motor
only some aspects, related to the mechanisms of the adhesion, ablation and
emission of smokes, are discussed in the following sections.
2.2. 1. Fundamentals of the mechanisms of
adhesion
In spite of the large number of studies dealing with the phenomenon of
adhesion during the past 40 years, the basic laws are relatively poorly known
and there is no unified theory capable of explaining the entire set of
phenomena [3,4].
One of the major difficulties is that adhesion is a multidisciplinary subject
requiring the collaboration of experts in the field of chemistry of polymers,
the physical chemistry of surfaces, the strength of materials, the mechanics of
fracture, and more. In addition, the number of parameters involved in a
theoretical modeling exceeds by far the analyses and computation capabili-
ties.
In spite of these somewhat pessimistic premises, bonding theories have
emerged. However, we must not forget that their scope is limited and that
their capability of prediction does not extend beyond a few typical and
particular fields.
2.2. 7. 7. Mechanical model
MacBain was the promoter of a mechanical model where the adhesion is
due to a fixing of the bonding agent to the roughness of the substratum.
MacBain’s research was done more specifically for the bonding of wood, and
although his model is in general no longer used, it is regaining interest
because of the recent research of Wake.
Broadly speaking, the roughness of the substratum is only a favorable
factor inasmuch as the wetting is sufficient. When that is not the case, the
portions that have not been wetted form the start of a break themselves. In
terms of adhesion between the liner and the propellant, mechanical linking is
used when adhesion is difficult, such as with propellants with low chemical
reactivity (cast double-base) or those which are highly plasticized (CMDB).
556 Jean-Michel Tauzia
2.2.1. 2. Electrical model
In 1948, Deriyagin and Krotova proposed a theory of adhesion based on
electrostatic phenomena observed during plucking tests on adhesives. Skin-
ner developed a similar theory in 1953. According to his theory, the system
constituted by the bonding agent and the substratum is compared to a
capacitator. For example, with an organic bonding agent and a metallic
substratum the metal can play the role of the electron donor and the polymer
that of the receiver, leading to the formation of a double electric layer.
The difficulties in developing a theory explaining the origin of the electric
charges are due to a lack of information about the levels of energy and about
the process of conduction in the polymers.
Although experimental work seems to confirm the validity of this model, it
is seriously criticized, and many authors agree in their opinion that the
electric effects observed are the consequence rather than the cause of a high
level of adhesion.
2.2. 1.3. The diffusion model
The Russian researcher, Voyustki, originated a theory according to which
the adhesion results from the diffusion of the molecules of the surfaces in
contact, creating a transition layer between the substratum and the bonding
agent. The plane interface is replaced by a spatial interphase. The reciprocal
solubility of the materials constituting the assembly is a primary condition
for obtaining a good bonding. Voyustki suggests, in addition, use of the
adhesion as a criterion for the thermodynamic compatibility of the polymers,
the best example of perfect compatibility being the self-adhesion of crude
rubber to itself, where the interface is quickly impossible to distinguish.
With this model the classic parameters of diffusion influence bonding
strength, including time, pressure, temperature, steric configuration of the
diffusing products and the crosslinking density of the substratum and, in the
case of polymers, they are the structural characteristics such as molecular
mass, morphology and crystallinity.
While the diffusion phenomenon is certainly important in the case of self-
adhesion, and for the bonding of polymers, it is difficult to imagine its
contribution in the case of bonding polymers to glass or metal. Schonborn
and Juntsberger, without refuting the existence of diffusion phenomena, feel
that they are subordinated to the process of putting in close contact, at the
molecular level, the materials to be bonded.
2.2. 1.4. Wetting model
In 1963, based on thermodynamic considerations and on the research done
by Zisman on the critical tension of the wetting of solids, Good, Fowkes and
Dann, and Sharp and Schonborn, developed and proposed a new model.
Thermal Insulations, Liners and Inhibitors
557
Since the bonding forces have a field of action on the order of the molecular
distances, a good bonding is created by an intimate contact between the
adhesive and the substratum, such a contact allowing the development of
these forces. This is in the occurrence, a criterion of proximity, involving the
cleanliness of the surfaces and a perfect wetting.
In this model the bonding energy can be determined, based on the surface
energies of the solids to be bonded and considering the wetting to be ideal.
Calculated in this manner, the bonding energy corresponds to the energy of
formation of the assembly. Experimentally, the debonding energy is often
considerably greater.
2.2. 1.5. Chemical model
Chemical adhesion involves chemical valence bondings between the adhe-
sives and the substratum. In spite of the obvious interest offered by this type
of mechanism, few studies have been done. It is true that demonstrating the
chemical reactions at the interface is particularly difficult.
As far as the bonding to propellant is concerned, it is noteworthy that
theories of chemical bonding are widely used to create specific molecules
known commonly as bonding promoters. These reactive products, exhibiting
low molecular mass, are carefully selected and introduced into the inhibitor.
They diffuse towards the interface where they react with the polymer of the
propellant to create stable chemical bondings, provided the wetting has been
done correctly.
2.2. 1.6. Model of the interfacial layer with weak cohesion
Bikerman, the author of this model, assumes that the probability of seeing
a rupture propagate itself exactly at the interface between the adhesive and
the bonded material is extremely low. From this premise it can be deduced
that the debonding occurs either in the adhesive or in the bonded material. In
fact, according to Bikerman, and more recently also to Sharpe, there is
another possibility: that of a debonding propagating itself in an interfacial
layer with weak cohesion. These authors distinguish several layers with weak
cohesion:
• a first layer consisting of air continues to exist at the interface (imperfect
wetting);
• other layers formed when foreign substances with low molecular mass,
contained in the adhesive or the bonded material, migrate to the
interface;
• yet other layers coming from a reaction between the atmosphere of the
ambient medium (humidity for instance) and the bonded material, or the
adhesive.
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Jean-Michel Tauzia
Although Bikerman’s analysis is also contested, it allows an explanation of a
number of observations made in the field of bonding. In particular it clarifies
greatly the role of water vapor absorbed by most of the surfaces.
As for the bonding of propellants on to combustion inhibitors, when
combined with the theories of the diffusion and chemical bonding, Biker-
man’s analysis allows the establishment of a conceptual frame within which
the technology used to perform the different bondings in rocket motors can
be developed.
2.2.2 . Fundamentals of the thermal protection
process through ablation
If the combustion chamber were to be directly exposed to the propellant
combustion gases, the weakening of the structure would lead unavoidably to
a rupture by bursting.
Should the inhibitors not play their role, the rapid heating of the propellant
would bring on an uncontrollable increase of the burning surface, with
consequences similar to those mentioned above.
In practice, the combustion chambers and the propellant grains must be
thermally protected against all excessive heating during the operation of the
motor. To provide this protection, organic materials coming into contact
with hot gases (2000-4000 K) protect the underlying areas through a
complex endothermic decomposition mechanism generally known as protec-
tion by ablation [5-8].
The temperature of the thermal protection rises by conduction until it
reaches its decomposition temperature by pyrolysis. This initiates highly
endothermic chemical reactions leading to the creation of gas and leaving a
sooty deposit, more or less porous, called “char”
A steady state establishes itself between the combustion gases and the
material in the process of pyrolysing. The pyrolysis front regresses. Once this
regression is finished, the heat absorption mechanism by thermal decomposi-
tion ceases. Only the char, inasmuch as there is any, continues to participate,
by conduction and radiation, in the protection of the underlying material.
It is important to note that these materials have a low thermal conductivity
which, combined with the short firing times, decreases the heating by
conduction of the protected parts.
2.2.2. 7. Examples of experimental test used to evaluate the
thermal characteristic of insulating materials
Several experimental systems are commonly used to compare the materials
among themselves or to measure the physical values necessary for modeling
the rate of ablation by computer analysis, using specially developed numeri-
cal programs.
Thermal Insulations, Liners and Inhibitors
559
“Extension firing ” (using an “exhaust pipe”). The tested materials are
placed in a pattern of a hexagonal base cone. They are mounted in pairs in
order to limit the dispersions caused by variations of the flow (Fig. 2).
Analysis of these results allows us to plot the ablation curves for a given
propellant, linking the ablation rate to the average speed of the flow of the
gases. These curves can be plotted for specific chamber temperatures, nature
of gases and time of exposure.
Firing of end-burning grains. With the end-burning grain system the
ablation can be measured on very low gas flow rates and for long firing times,
which is not feasible with exhaust pipe firing. Analysis of the tests results in a
curve linking the ablated thickness to the firing time.
The plasma torch. The plasma torch is also used. It allows us to know the
behavior of different materials.
Finally, conventional differential thermal analysis (determination of the
ablation enthalpy) and thermogravimetric analysis permit the completion of
the data used to predict the ablation rate, thanks to numerical programs.
Fig. 13.2. Firing test designed to evaluate the ablation rate of thermal insulations.
2.2.3 . Fundamentals of optical phenomena
related to the operation of a rocket motor
The emission of smoke or flashes by rocket motors is a critical factor for
many missile systems [9,10]. The release of smoke reveals the location of the
launcher. A smoke trail makes the trajectory of the missile visible at great
distances, giving the target the possibility of escape. For wire-guided missiles
the plume greatly reduces visibility conditions. The presence of solid particles
in the plume may hinder the functioning of the guiding device. The presence
of flashes may interfere with tracking systems located on the firing pad.
560
Jean-Michel Tauzia
2.2.3. 1. Fundamentals of the smoke phenomena
Smoke may be defined as a condensed liquid or solid phase, in suspension
in air. There are, usually, two categories:
• condensation smoke;
• dispersion smoke, formed by the subdivision of very fine particles.
In rocket propulsion the dispersion smoke composed mainly by metallic or
refractory particles results from the combustion of the propellant and the
pyrolysis of the insulating materials, while condensation smoke comes from
low-mass organic molecules existing as vapor in the plume that condenses
during the rapid cooling following expansion of the gases in the nozzle.
2.2.3. 2. Visibility of an object as a function of the contrast
The visibility threshold of an object is usually expressed in terms of
contrast. When an object moves away from the observer, the contrast
decreases because of atmospheric absorption. At a fixed distance between the
observer and the target, when the luminosity increases, the contrast also
increases because the target is more luminous than its background and the
opposite occurs when the target is less luminous. Consequently, the plume of
a missile is more or less visible whether the missile flies over grassy ground,
the sea, or toward the sky.
2. 2.3.3. Opacity of the smoke
Visibility of an object through a smoke plume varies according to the
manner in which the particles reflect, diffuse or absorb light. The main
parameters are morphology, size and density of particles, refraction index
and wavelength of incident light.
The opacity of the smoke can be reduced by decreasing the number of
particles released, as well as their size, until reaching a diameter much lower
than the wavelength of the incident light.
2. 2.3.4. Duration of the smoke
Experiments, full-size, have demonstrated that losing sight of a target for
1-2 s is sufficient for the launcher to lose control of the missile. Conversely, a
rapid dispersion of the smoke — in less than 1 s — may be compatible with
efficient tracking systems.
2.2.3. 5. Development of smokeless motors
Insulating materials must be considered as potential sources of smoke
which are particularly inconvenient when the propellant has been selected on
Thermal Insulations, Liners and Inhibitors 561
the basis of its low signature. There are, however, two categories of inert
materials with low or no signature:
• Low or no signature materials due to the fact that no particles are ejected:
the “particles” released during their pyrolysis are mainly gaseous, or non-
condensable, or very small. This goal can be achieved by using organic
materials without refractory fillers.
• The highly refractory materials for which solid particles formed during
the pyrolysis are few in number and stay in the combustion chamber.
2.2.3.6. Flashes emitted by the rocket motors
These flashes come from the plume made of heated gases released by the
nozzle or from reignition (postcombustion), caused by recombination with
the oxygen of reducers contained in the gases. Attenuation of the flashes is
usually obtained by introducing appropriate ions in the combustion gases,
capable of blocking the recombination reactions that involve free radicals
(Chapter 5).
These ions may be contained in the propellant itself, or if the design of the
motor allows it, in the inert material subjected to a controlled pyrolysis
during the operation of the motor.
2.2.3. 7. Experimental methods for the measurement of smoke
Because of the complexity of the phenomena involved, experiments have
been conducted during the firing of motors consisting of a cylindrical end
burning grain, inhibited laterally and on the front-end surface with the
material being tested and for which the grain has been carefully selected,
based on its own very low signature, previously measured by firing of non-
inhibited grains.
The observations deal primarily with the opacity of the smoke. An
experimental device, called an opacimeter, allows us to measure the attenua-
tion in the axis of the jet as well as perpendicular to it, while a film is being
taken using a luminous background made of selected color patterns.
2.2.4. Combustion of the propellant along the
inhibitor
In the vicinity of the bonding of the propellant and the inhibitor a large
number of physicochemical phenomena may occur, which influence the
burning rate of the propellant. This alteration is felt particularly for end-
burning grains where the existence of a local increase of the burning rate
562
Jean-Michel Tauzia
along the inhibitor may have a strong effect on the pressure and thrust curves
[1,2]. This burning rate increase may be the result of:
• heating of the propellant under the inhibitor, due to the circulation of
heated gases in the clearance between the chamber and the grain;
• segregation of the fine oxidizer particles in the vicinity of the inhibitor,
caused by decanting-type mechanisms — this possibility exists only in the
case of grains cast in their inhibitors;
• existence in the liner of compounds which are ballistic modifiers (iron
oxide);
• existence of vacuums or microscopic cracks;
• alteration of the local composition of the propellant through the migra-
tion of mobile molecules towards and from the inhibitor (plasticizers,
crosslinking agents, liquid combustion catalysts and others);
• local variations in the radiation density of the flame in the vicinity of the
inhibitor.
For instance, if the plasticizer of a propellant can migrate to the inhibitor,
the propellant close to the inhibitor appears, locally, richer in oxidizing
species. This results in an increase in the burning rate as well as in the
pressure exponent, so that the burning rate enhancement grows with
propellant temperature and operating pressure of the motor.
To minimize this phenomenon the grain designer selects materials that are
impermeable to the mobile components of the propellants and balances, a
priori , the chemical potentials on each side of the bonding surface. When
equilibrium cannot be obtained, he may, on the other hand, introduce into
the inhibitor a plasticizer moderating the burning rate of the propellant.
2.2.5. Method of prediction of the aging of the
bonding
As with all other components of the rocket motors, the insulating materials
must ensure complete operation for the duration of the service life of the
motor. Among these, the “bonding” function is certainly the most sensitive to
aging.
The aging of the bonding is caused by the development of chemical
reactions, complicated by diffusion phenomena. Each of these reactions
exhibits an activation energy which, lacking a more precise theoretical model,
can be idealized by an Arrhenius-type law. The aging is evaluated by
comparisons of results recorded at ambient temperature at various stages
with results recorded at moderate temperatures ranging from 40 to 50°C. The
raw materials themselves need to be perfectly stable during the period of time
considered.
Accelerated aging experiments on complex materials need to be performed
with the greatest circumspection because they usually tend to overestimate.
Thermal Insulations. Liners and Inhibitors
563
2.2.6 . Pyrotechnical compatibility — selection of
the raw materials
The raw materials of the insulating materials for combustion chambers
must be chemically compatible with the energetic ingredients of the propel-
lants (mineral oxides, nitrated plasticizers, explosives, nitramines and others).
Two tests are currently performed for this purpose:
• Differential thermal analysis, where the research worker subjects the
energetic ingredient, in powder form and in the presence of the material
being tested, to a regular increase of temperature. The verdict is made on
the basis of the modification of the decomposition temperature of the live
ingredient.
• The “vacuum test”, where the tester puts together, in powder form under
heat and vacuum, the live ingredient and the inert materials for testing.
The verdict is made on the basis of the volume of gas produced as well as
on its rate of production.
2.2. 7. Criteria for the selection of raw materials
used in the formulation of insulating materials
There are many considerations that are principal factors in the develop-
ment of insulating materials to obtain satisfactory mechanical properties,
bonding and other design goals, while other data limit the choice of the
designer (for example, pyrotechnical compatibility). In particular, the raw
materials must satisfy the following conditions:
• guaranteed availability over a sufficient period of time;
• stability over time;
• reproducibility of the production, process including the control of the
impurities coming from the raw materials.
2.3. DETERMINATION OF THE CHARACTERISTICS OF THE
BONDING PERFORMANCE OF INSULATING MATERIALS
Once the formulation of an inhibitor has been selected, based on the
general rules discussed above, it is necessary to determine its performance.
The mechanical characteristics of inert materials are measured: For a rapid
determination of these characteristics the tests are performed at ambient
temperature, with tensile loading rates of 50 mm/min, while a complete
characterization requires the tests to be performed with several loading
rates (from 1 to 1000 mm/min) and several temperatures ( — 40°C, +40°C,
+ 60°C).
The bonding characteristics are determined by carrying out tensile, shear-
ing and peel tests.
564
Jean-Michel Tauzia
We should note here that the bondings between the insulating material and
the propellant behave more or less like their constitutive components, and
that, as a result, bonding master curves can be plotted.
The methods selected to design a rocket motor are based on results from
tensile and shear tests, since all types of loading involved can be reduced into
these two basic stress/strain modes. The peel test, on the other hand, although
not used in the determination of the stress and strains of the grain, is widely
used for two main reasons:
• peeling is a test of resistance to tearing that simulates very well what
occurs at the ends of the grain;
• peeling can be considered as an indication of the quality of the bonding.
2.4. OPTIMIZATION OF INSULATING MATERIALS
The formulation’s analysis is done by taking into account the rules of the
art and previous experience, and also by performing, during the initial phase,
various tests using a wide range of parameters likely to provide the desired
performance in order to select the most promising results.
This phase may require a long time. It is also the most difficult one because
intuition plays an important role. It leads to selection of a family of
formulations that is the first approximation of the composition desired.
Two distinct activities will then take place in close relation to each other;
one involving the formulation itself and the other the manufacturing pro-
cesses. When this work is completed, the formulator is able to define the
limits of the composition and the acceptable variations of the raw materials
and production processes that can be used to maintain constant properties of
the material.
A third phase consists in testing the reproducibility and the aging, after
which the industrial documentation is completed.
2.5. MOST COMMONLY EXPERIENCED FAILURES
The type of failure most often observed on a rocket motor involves the
bonding between the inhibitor or the liner and the propellant. This may be
attributed to the significant variability of the materials used and, to an even
greater extent, to the variability of the bondings. The latter problem may be
accentuated by anomalies occurring during manufacture:
• insufficient prevention against the environment at the time of preparation
of the materials and the actual bonding;
• insufficient knowledge of the raw materials, which may contain impurities
such as adhesion poisons;
Thermal Insulations, Liners and Inhibitors
565
• insufficient knowledge of the solubility and diffusion properties which
cause undesirable chemicals (from a bonding point of view) to migrate
and localize at the interfaces (live or inert plasticizers);
• insufficient knowledge of the rates at which the bonding develops
resulting in premature stresses and strains in the bonding.
To take precautions against such anomalies it is important to perform, at
the commencement of the development of an insulating material, full-size
experiments, accelerated aging and overtests, complemented by surveys, so
that the real results obtained may be compared to the laboratory tests.
2.6. QUALITY INSPECTION OF BONDINGS
The techniques used to create the bondings today are even more similar to
an art that has reached a certain level of maturity than they are to an exact
science. Consequently, it is not always sufficient to select the raw materials
carefully, and to combine them using a strictly defined process to guarantee
that all required specifications are met.
The manufacturer must therefore be able to evaluate by non-destructive
means the quality of the work done, in order to discover anomalies such as
voids, debonding and porosities. There are numerous non-destructive tests
that can be applied to bondings, although only two are widely used for
industrial applications. These are described below.
2. 6. 1. Quality inspection of bondings by X-ray
X-rays, using mainly the usually small differences in the density of the
various materials, are able to detect debonding only when there is some
separation between the materials. However, since X-ray systems generally use
powerful generators, sensitive emulsions and highly trained operators, a very
high proportion of failures are identified. In addition, it is possible to improve
the global resolution power of the method by varying the stress condition of
the area examined (moderate cooling of the suspect area, for example).
New technology such as image processing or new analysis tools, such as
tomography and Compton scattering, may improve the sensitivity and
reliability of this quality inspection technique which, in any case, is not
capable of differentiating between a good bonding and a poor one. Finally,
video radioscopy, also slightly less sensitive, allows us to increase signifi-
cantly the productivity of non-destructive inspection operations.
2 . 6.2. Control of bondings by ultrasound
The propagation of ultrasounds inside materials is disturbed when the
beam meets an interface or a heterogeneity. Analysis of the signals received
566
Jean-Michel Tauzia
allows us to perform insurance quality of the bondings. This is a fairly
complex task and requires both favorable testing conditions, such as the
possibility of using a coupling liquid, and experienced operators.
This method is used mostly with small free-standing grains, in addition to
X-rays.
3. Processing Insulating Materials
3.1. INHIBITING PROCESS OF FREE-STANDING GRAINS
The most simple process to inhibit free-standing grains is coating them by
casting into a mold.
One method widely used with long pot-life materials consists of mixing all
the ingredients in a vertical mixer with a bowl fitted out to allow the injection
of the uncured insulator into several molds assembled on a plate distributing
the inhibitor.
Another method involves casting the grain inside an inhibiting material
(inhibiting tube or restrictor) previously shaped, either through the extrusion
process (in the case of a thermoplastic material) or by pressure molding,
either with a press or in an autoclave (in the case of a rubber material).
Other basic processes are sometimes used, their selection being often
dictated by technical or economical constraints:
• Wrapping ethylcellulose tapes on extruded or cast grain of double-base
propellant.
• Soaking of propellant grain in an inhibiting solution. This technique is
acceptable only for small objects such as the strands used in the strand-
burner test.
• Pushing the propellant grain into a mold containing at the bottom an
appropriate quantity of uncured inhibitor.
• Spraying on the propellant grain with a material exhibiting appropriate
rheological characteristics.
Except for the first process mentioned, these principles have not been widely
developed in the industry.
3.2. PROCESS OF PREPARATION OF THE CASES FOR CASE-
BONDED GRAINS
A case-bonded grain includes, in addition to the case, thermal protection,
liner and devices designed to accommodate the nozzle.
The application of the liner will be described in detail, while only brief
indications will be given concerning the thermal protection.
Thermal Insulations, Liners and Inhibitors 567
3.2. 1. Fitting the thermal protection into the case
For metallic motor cases the thermal protection components, consisting of
polymers reinforced with cooling or refractory fillers, are molded in their final
form and then bonded inside the case. The adhesives used must give the
bonding characteristics required and also be easy and foolproof to apply.
When the cases are obtained through filament winding, the composite is
frequently wound around a destructible mandrel coated with the uncured
thermal protection. The entire assembly is placed in an oven, both to
polymerize the composite and to cure the thermal rubber.
The thermal insulation is often provided with stress relief devices designed
to reduce the stresses in the bonding surfaces of case-bonded grains. These
features are also known as relief flaps.
3.2.2. Preparation of the case and the liner
3.2.2. 1. Inspection of the cleanliness and dryness of the
thermal insulation
It is necessary, to obtain a good bonding, to proceed to the coating on a
clean surface.
Wetting tests reveal possible pollution of the surface. In such a case,
cleaning (grease removal) operations must be performed again, involving if
necessary a mechanical sandblasting before continuing the equipment of the
case.
Another important point is the complete absence of humidity. The
presence of water may hinder the bonding of the liner to the thermal
protection, and later on, also of the propellant to the liner.
3.2. 2.2. Preparation of the liner
The preparation of the liner can be made in one step (one shot) in a mixer
of a type similar to those used for the mixing of the propellant. Such a
technique is possible only when the pot-life of the liner is sufficient to allow all
sequences of the laying process to be completed. For this purpose, the use of
“blocked catalysts” is particularly well-indicated [13,14], or better yet, the
use of a blocked curing agent which is thermally activated [15].
The use of liners diluted in a solvent artificially increases the pot-life and
facilitates the spraying. Attractive in principle, this process allows only the
spraying of thin layers.
The liner may also be prepared in the form of a material with two
components which are mixed at the last moment at the site of coating, using
precision automatic feeding equipment. The control of the flow rate of the
components requires a high and instantaneous precision. Although many
568
Jean-Michel Tauzia
quantity measuring and mixing machines exist on the market, few of them
offer the required characteristics and they need to be adapted to meet specific
requirements: flow control with the required level of precision, for limited
rates of throughput of the order of 50 g/min, while keeping track of the data
of operations already performed. The combined use of sufficiently sensitive
gages and computer controls allows these requirements to be satisfied
[16,17],
3.2.3 . Application of the liner to the cases
3.2.3. 1. Coating the liner by centrifugation
The principle of the centrifugation process consists of introducing the liner
in a liquid state at the bottom of the case and proceeding to polymerization
by subjecting the case to a rapid spinning, which plates the liner against the
wall of the motor. The operation, thanks to specially designed machines, can
be performed for the cylindrical motor case and the front- and aft-ends.
Today, this process is being replaced by spraying, which allows reduction of
the inert mass involved, and improvement of the propellant mass fraction of
the motor.
3.2. 3.2. Coating the finer by spraying
The “spraying process” involves spraying the liner in a liquid state in fine
droplets onto the inner surface of the case before the crosslinking reaction has
taken place. The spraying system, and if necessary the case, must be activated
to be moved in relation to each other to ensure that the required thickness of
layers of liner is deposited at the right places.
Many systems are used in the industry for the spraying of liquids:
• blowing by compressed air of a liquid jet: pneumatic spraying (Fig. 3);
• sudden expansion of liquid under pressure: airless spraying;
• blowing by centrifugal force with a device such as a disk or a bowl
spinning at high speed (Fig. 4).
The blowing of the product can be facilited with the use of a device
generating electrostatic charges: “electrostatic spraying heads”.
The liner spraying systems are derived from commercial equipment.
However, it was necessary to redesign them completely to adapt them to
using uncured liners exhibiting extremely high viscosities. At the same time
they were miniaturized, so that today it is possible to coat cases with an
insides diameter of 40 mm.
Thermal Insulations, Liners and Inhibitors
Oven
569
Fig. 13.3. Device used to spray the uncured liner into the case (pneumatic spraying).
3.2.4. Application of a liner with mechanical
embedment
When faced with difficult bondings, as might be the case with highly
plasticized propellants, an improvement consists in embedding the liner with
particles — typically cylindrical particles — which permit a mechanical em-
bedment between the liner and the propellant [18]. This incrustation can be
done by pneumatic spraying of particles on the liner while it is still uncured.
570
Jean-Michel Tauzia
The peel test value of the embedded liner in peel tests is multiplied by a
factor of 2 to 3. The incrustations constitute some sort of obstacle to the
propagation of tear caused by peeling.
3.2.5. Recycling of the coated cases with a cured
liner out of specifications
Defects may be present in the materials or the bondings in a case, and they
must be detected before proceeding to the casting of the propellant. When the
defect cannot be corrected it is desirable to be able to recycle the case. Several
techniques are available:
• Prolonged soaking in a solvent, causing a swelling of the materials, which
can later be removed by mechanical brushing.
• Removal of the material with a high-pressure water jet. This technique
cannot be used with composite materials because it would cause irrever-
sible damage to the case.
• Removal of the material with a heating device locally weakening the
mechanical properties of the material to be removed.
• Dissolving the liner to be removed with a solvent selected not to attack
the other inert materials present in the case.
4. Examples of Insulating Materials Used In
Rocket Propulsion
While the compositions of propellants developed in various countries have
a pronounced similarity, due as much to energetic considerations as to the
availability of raw materials, the diversity of insulating materials (e.g.
polyurethanes, epoxides, silicones, synthetic rubbers and phenolic resins),
precludes trying to be exhaustive or even provide detailed descriptions of
each type.
For the several examples dealt with in the following sections, reference is
made whenever possible to patents and papers listed in the bibliography,
particularly when it concerns the chemical aspect of the materials [19].
4.1. INHIBITING MATERIALS FOR FREE-STANDING GRAINS
4.1.1 . Cast inhibitors
Inhibiting by casting over a propellant grain is interesting in particular for
small grains. Nevertheless, some large grains are still produced using this
technique.
Thermal Insulations, Liners and Inhibitors
571
4. 1.1.1. Cast inhibitors for composite propellants
This technique is not much used in actual production. The materials used
have been prepared based on propellant binders — particularly when it
involves polyurethane — correctly adjusted in terms of the crosslinking rate
and final mechanical properties.
Polyurethanes, although exhibiting good bonding characteristics — parti-
cularly with the peel test — are expensive to produce due to their sensitivity
to humidity, and epoxide-based inhibitors are being preferred whenever their
mechanical and bonding properties are deemed sufficient for the selected
application.
4. 1. 1.2. Cast inhibitors for extruded or cast double-base
propellants (Table 1)
Most elastomers which can be crosslinked at low temperature are potential
materials for the formulation of cast inhibitors: unsaturated polyesters and
silicones curing at ambient temperature, polyurethanes, polysulfides and
epoxides can be used. In fact, the selection of one over the other is based on
constraints related to the operational mode of the motor and the exact
composition of the propellant used.
Table 1 lists the major characteristics of various cast inhibitors belonging
to the three most commonly used families, which are briefly described in the
following sections.
4. 1. 1.3. Unsaturated polyester
Polyesters are made of unsaturated polymer chains diluted in styrene and
capable of crosslinking by free-radical-type reactions with the assistance of
appropriate catalysts and accelerators.
The polymer is usually blended with refractionary fillers designed to
improve the thermal resistance. At the manufacturing level their low initial
viscosity makes them ideal for casting, but they can also just as easily be
injected with precision automatic feeding equipment.
This family of inhibitors was developed very early, in the 1950s [20], and is
still widely used. Its known limitations are related to a high smoke emission,
attributable to high amounts of aromatic products contained in the formula-
tion, as well as a propensity — that could be high depending on the type of
propellant used — to swell in contact with nitrated plasticizers. The swelling
alters the mechanical properties of the material and shortens its service life.
Improvements have been obtained by:
• using a primer of the triisocyanate type which, by reducing the rate of
migration of nitroglycerine, reduces the swelling;
Table 1 Major characteristics of cast inhibitors for extruded or cast double-base propellants
572
Jean-Michel Tauzia
PU 003 7.3 596 30 -40°C 0.40 1.10
+ 20°C 1.30 1.68 1.30 yes 40 90-92
+ 60°C 1.82 1.96
Table 1 ( continued )
Thermal Insulations, Liners and Inhibitors
573
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574 Jean-Michel Tauzia
• introducing polymer chains with halogen atoms [2] and also reducing
and even removing the aromatic diluents which increase the smoke
signature.
4. 7. 7.4. Silicone inhibitors: an excellent inhibiting material
once the bonding problems are under control
Silicone inhibitors are produced from polydimethylsiloxane-reactive oils,
crosslinking through a condensation mechanism under the influence of the
appropriate catalysts. They contain refractory fillers and fibers which lead to
the formation, during firing, of a solid char which retains the particles in the
combustion chamber of the motor. This factor, combined with the absence of
tar formation by condensation, imparts a very low signature to silicone
inhibitors.
This family of inhibitors has other specific characteristics such as the
absence of any absorption of nitrated plasticizers, giving it a good stability for
all of its physical characteristics, such as mechanical properties, shape, etc.
Unfortunately, silicones have a low natural propensity to adhesion on the
propellant. The remedy consists usually in using a primer based on a
functional silane. The use of such a primer, however, is not economical or
desirable in terms of reliability of the bonding.
In France, self-adhesives, particularly high-performing polydimethylsilox-
anes, were developed. The process that permits self-adherence is a direct
application of the theory of chemical bonding at the interface.
All relevant details on this family of inhibitors are contained in references
[10] and [22], which provide a complete review of the chemistry, the
performance and the characteristics of production of silicone-based inhibi-
tors.
4. 7. 7.5. Polyurethane inhibitors; generating only gases during
a thermal decomposition (organic inhibitors)
In this class of inhibitors are grouped materials that are made from
polymers with a saturated and oxygenized chain without mineral refractory
fillers (or with submicron particle sizes). These materials decompose by
pyrolysis, preferably in a gaseous form with a minimum formation of soots
and tars.
From the binders currently available for elastomers able to crosslink at low
temperature, polyethers or hydroxylated polyesters are the best candidates to
fullfill the required criteria.
In the case of crosslinking by isocyanates, a first study points to hydroxy-
lated resins with polyoxyethylenic and polyoxypropylenic chains, with a
carbon versus oxygen ratio of 2 and 3, respectively. In practice, however, the
best compromise between a low signature and thermal resistance is obtained
Thermal Insulations. Liners and Inhibitors 575
with polymers made by opening C4 or C5 rings including oxygen [23] and
further progress is still being made.
The possibilities for choice of refractory fillers are more limited, inasmuch
as there is not a great number of highly oxygenized thermostable organic
products. Oxamide appears to be the best one; but in the case where the
thermal resistance would prove to be insufficient, a dense mineral filler, with
appropriate particle size and capable of providing oxygen, can be added.
Another means consists of incorporating into the formulations a low
quantity of fibrous mineral or organic filler. The ablation ratios are improved
by 20-25% and the signature properties are not altered [24]. The viscosity of
the mixtures continues to be compatible with injection casting.
Injection with precision automatic feeding equipment at high or low
pressure makes it possible to reduce the cost of inhibiting, particularly for
high rates of production. However, this manufacturing process requires a
formulation of inhibiting composition based on two components preferably
exhibiting similar viscosities and equivalent masses.
4 . 1.1. 6. Future cast inhibitors
It seems that some applications, such as rocket motors for antitank
missiles, will continue to use free-standing grains inhibited by cast inhibitors
for a long time. The future ideal inhibitor should combine the simplicity of
the polyester, the stability of the silicone and the low signature and excellent
bonding of the polyurethane. A compromise of this sort is not easy to come
by, although the epoxide systems cured at low temperature, handicapped for
a very long time by the low pyrotechnic compatibility of the amine curing
agent, may hold the key to future progress. Methods have been recently
found that are both easy and may be industrially feasible, allowing the use of
curing agents in the presence of double-base propellants, which offers
prospects of development attractive in terms of cost and performance.
4. 1.2. Restrictors for free-standing grains
Restrictors are made from elastomeric material presenting sufficient ther-
mal resistance (polyvinyl chloride, thermoplastic rubber or synthetic rubber)
molded in advance with the external shape of the grain into which the
propellant in its slurry form is cast before curing. This process results in a
particularly economic manufacture. It requires the use of elastomers selected
for their adhesive properties with the propellant (such as EPDM rubber or
butyl in the case of composite propellant with polyurethane binder) or their
low signature, for cast double-base propellants. A reader interested in this
particular area will find numerous details on the composition of restrictors
for composite propellants in reference [25] or double-base propellants in
[26] and [27].
576
Jean-Michel Tauzia
4.2. LINERS FOR CASE-BONDED GRAINS
Free-standing grains do not permit the construction of motors with large
diameters. The development of case-bonded technology provided an answer
to this need.
This is not the place for an historical review of the development of this
process. Interested readers may refer to articles listed in the bibliography
[28-30]. But the emergence of this motor design led to the development of a
new elastomer material, called binding material or liner, designed to ensure
the mechanical bond between the case and the propellant or between the
thermal protection and the propellant. In the beginning, the adhesion
between the liner and propellant was obtained by keeping the same binder for
both materials. Without a doubt this was done to have the best thermodyn-
amic compatibility possible, as well as sufficient wetting of the interface.
Later, research demonstrated that the optimum binding was often obtained
with a chemical composition of the liner that was different from that of the
propellant binder.
The following factors play an important role in the creation of the binding:
• curing level of the liner at the moment when the propellant is cast:
presence or not of reactive chemical functions;
• presence in the liner of chemical species capable of diffusing and of
chemically binding with the propellant binder: presence of adhesion
promoters;
• crosslinking density of the liner: allowing sterically the thermodynami-
cally possible diffusion.
4.2. 1. Detailed formulation of a liner for a
propellant with a CTPB binder (Table 2)
The base polymer will be a polybutadiene in order to ensure good
thermodynamic compatibility. For reasons of reactivity and low viscosity, a
hydroxytelechelic (HTPB)-type polybutadiene was selected; and to be able to
tailor the mechanical properties, a hydroxylated chain extensor with low
mass was added to the prepolymer.
A mineral filler (carbon black, titanium oxide) also regulates the mechani-
cal characteristics, increases mechanical resistance and controls the rheology
of the material before polymerization. The stoichiometric ratio allows
adjustment of the level of the mechanical properties with great precision.
In order to ensure a high level of adhesion between the liner and the
propellant, the liner will include an adhesion promoter capable of creating
linkage through covalent bonds at the interfaces.
Finally, a catalytic system will not only allow control of the rate of
crosslinking but also, in some cases, will control the nature of the chemical
reactions at the interfaces.
Thermal Insulations, Liners and Inhibitors
577
Table 2 Composition and characteristics of a liner designed for an aluminized composite
propellant using a CTPB binder
Physical properties of the liner
Density at 20°C
1.14
Electrical resistivity
10 12 fim
Linear thermal expansion coefficient
120 io- 6 / 0 c
Specific heat
0.4 Cal/g
Composition of the liner
HTPB
66.0%
Chain extender
8.0
Antioxidizer
0.3
Bonding promoter
3.6
Filler
13.0
Crosslinking agent
8.6
Catalyst
0.5
Pot-life— 20 min at 20°C
Mechanical properties of the liner*
Temperature
+ 20°C
S m (MPa)
2.2
(%)
250
E (MPa)
0.8
e m (%)
800
e,(X)
800
Bonding properties
C - shear strength (MPa)
0.65
T = tensile strength (MPa)
0.65
P = peeling strength (daN/cm)
2.5
a Tensile loading rate 20 mm/min.
b Test rate 10 mm/min.
Test temperature 20°C.
Of course, the propellant will be cast on a liner that is not completely
cured, to facilitate the adhesion, and that is free of poisons such as absorbed
water, tensio-active agents, etc.
The selection of the set-point is made by using a methodology that allows
us to localize rationally the optimum of a function of several variables
(experimental design factorial studies).
Table 2 provides the composition and the major characteristics of a liner
for composite propellant (CTPB binder).
4 . 2 . 2 . Other examples of liner development in
response to specific situations
For the most part, the general ideas proposed in relation to the develop-
ment of a liner for CTPB liner propellant are also true for the other types of
578 Jean-Michel Tauzia
binders. However, particular situations arise where special requirements are
needed.
For instance, a propellant may, because of its composition, be sensitive to
electrostatic discharges. In this case appropriate precautions must be taken to
eliminate the risks during the manufacture or handling of the grains. Such
precautions include, for example, devices to eliminate the charges and
equipotentiality of all elements. A specific means of protection consists, for
instance, of building a Faraday cage around the grain, thereby eliminating all
outside influences. A family of conductive lines has been developed for this
purpose. Their extreme viscosity in the uncured state required the develop-
ment of highly original spraying systems.
4.2.3. Liners designed for tactical case-bonded
grains manufactured at high rates of production
The development of case-bonded propellant grains in tactical missiles was
a consequence of requirements for high propulsion performances.
A review of possible concepts has been published by E. Gonzales and F.
Marks [31], which demonstrates the usefulness of taking into account, in
particular, the inert components of the motor.
Similarly, R. T. Davis and J. D. Byrd pointed out the economic advantages
expected from the use of a liner with a blocked isocyanate as a crosslinking
agent [15].
These types of liners have been developed in France during recent years.
They have a pseudo-plastic behavior which eliminates all risks of dripping
during manufacture, and crosslink through the use of a blocked isocyanate
linked to an appropriate catalytic system.
The selection of the blocked isocyanate was made in such a way that it not
only contributes to a very long pot-life at ambient temperature, but also
provides (during the deblocking through thermal activation at 60°C — in
particular during the curing of the propellant) the isocyanate functions
allowing an improvement of the cohesion at the interface between liner and
propellant. In addition, the blocking agent acts as a plasticizer for the
propellant, improving the binding behavior at low temperature.
In terms of mass production, the very long pot-life results in a great
flexibility of use, significantly reducing manufacturing cost.
4.2.4. Liners designed for grains using propellant
with high levels of nitrated plasticizers (XLDB)
In terms of their compositions these propellants resemble the conventional
composite propellants already discussed in this chapter, with several addi-
tional particularities (undesirable in terms of bonding) linked essentially to
the presence of a significant quantity of nitrated plasticizer.
Thermal Insulations, Liners and Inhibitors
579
The liners are similar in their composition, as well as in the quality control
methods, to those we just examined. However, in order to improve peel
behavior a form of mechanical linking, known as mechanical embedment
[18], was used in the past. Recently, with the purpose of simplifying the
process, improving the reliability of the bonds between the liner and the
propellant and reducing the costs, a family of liners with direct bonding has
been developed.
4.3. THERMAL PROTECTION DESIGNED FOR THE
INSULATION OF COMBUSTION CHAMBERS
Excellent descriptions of these materials are available in the bibliography
[32,33] or in commercial brochures [34]. Protection through the ablation
mechanism was described earlier. We will therefore limit ourselves here to
pointing out that the elastomers used to manufacture flexible thermal
protection are most often made of rubber (NBR, NR, EPDM and Hypalon)
with cooling fillers (oxalate, carbonate and hydrate) and refractory charges
such as carbon, silica or asbestos fibers. In contrast, the majority of the rigid
thermal protections are made of phenolic resins (or derivatives) reinforced
with refractory fibers such as asbestos, silica, carbon, alumina or even nylon.
The selection is always guided by the particular characteristics required for
good operation of the motor.
However, the thermal protection for integral boosters located in the
propulsion chamber of a missile powered by a ramjet calls for special
attention in this section.
The reader may find in this book, as well as in the bibliography, pertinent
information about the functioning of these ramjets [35].
The point that needs to be emphasized here has to be with the fact that the
material ensuring the bonding of the propellant to the case during the boost
phase of the missile must also later work as the thermal protection of the
combustion chamber of the ramjet. Consequently, this thermal protection
must have the usual performance characteristics of a liner. In particular, it
must be sufficiently elastic to withstand, without breaking, the deformation
induced by the operation at high pressure of the booster grain. This virtually
forbids the use of phenolic compounds reinforced with silica. Of course, the
elastomer selected must withstand the oxidizing atmosphere of the ramjet
combustion chamber without burning.
Because of these two requirements, the number of choices is drastically
limited. Only polysiloxanes (or derivative materials) are capable of satisfying
all of these specifications. Table 3 gives the composition and main character-
istics of such a thermal protection.
However, the siloxanic materials due to their very low critical wetting
tension (the second lowest after PFTE) have a very poor natural adhesion
with the propellant. This resulted, in the United States in particular, in the
580 Jean-Michel Tauzia
Table 3 Major characteristics of a thermal protection for integral booster for a ramjet
missile
Physical characteristics , at 20° C
Density at 20°C
1.45
Electrical resistivity
10 6 nm
Linear Thermal expansion coefficient
4.7 x 10" 4 .K"
i
Thermal conducitivty
0.40 W/°C m
Specific heat
1.13 J/°C
Composition
Bicomponent silicone elastomer
RTV type
46%
Granular refractory charge
23%
Fibrous refractory charge
18%
Catalyst
7.0%
Mechanical characteristics a
Temperature S m (MPa) (%)
E (MPa)
«.(%)
e , (%)
— 40°C 5.6 4.6
122.0
55
55
+ 20°C 4.7 3.8
138.0
51
51
+ 60°C 4.5 4.6
96.0
52
52
Bonding characteristics 0
Shear
Tensile
Peeling
strength
strength
strength
(MPa)
(MPa)
(daN/cm)
HTPB Composite propellant with liquid
burning rate modifier
6.5
7.5
1.5
Aluminized HTPB composite propellant
5.0
7.0
2.0
a Tensile loading rate 50 mm/min.
b Test rate 10 mm/min.
Test temperature 20°C.
development of complex solutions to ensure the bonding of the booster grain
to the chamber [36].
In France, the research was oriented in two directions:
• improvement and simplification of the bonding techniques of the integral
booster in the combustion chamber of the ramjet;
• improvement of the thermal performance of the material in terms of a
decrease in thermal conductivity and a rise of mechanical strengthening
of the residual char, to make it capable of withstanding flow instabilities
in the combustion chamber of the ramjet.
To improve the bonding of the propellant to the thermal insulation much
attention has been paid to the chemistry of the propellant binder.
Thermal Insulations. Liners and Inhibitors
581
HTPB, which is used to manufacture the propellant of the booster,
crosslinks through a reaction of the isocyanate functions on mobile hydro-
gens. Advantage has been taken of this reaction in the selection of polydi-
methylsiloxane as a binder for the thermal protection, and to introduce in the
latter adhesion promoters, such as functional silane or blocked isocyanates.
These chemicals improve the bonding by creating strong chemical links at the
interfaces with the propellants. The result is that the propellant may be
directly bonded onto the thermal protection. Among other things, this solves
the problem of combustion of residues at the transition between the boost
phase and the operation of the ramjet chamber.
Simultaneously, an improvement of the mechanical strength of the pyro-
lyzed portion is attempted by using polymers leading to a higher amount of
ceramic-like residues than with polydimethylsiloxanes, and by increasing the
efficiency of the endothermic reactions during the exposure of the thermal
protection to a high heat flux. Significant progress has. been made in the
following areas:
• use of fibrous refractory reinforcements to improve the thermomechani-
cal resistance of the char;
• use of polymers similar in type to those used as precursor for the
production of silicium carbide fibers;
• use of polysilarylene-polysiloxane as a replacement for polydimethylsi-
loxane as a binder for the thermal protection material, leading to a
significantly higher amount of refractory residues [37].
5. Conclusion
This chapter, devoted to insulating materials for propellant motors, shows
that the preparation of a case or the inhibition of a grain are very complex
tasks, because they must reach a fine compromise between a large number of
often contradictory requirements.
The reader will have noted that making the appropriate materials available
to the designer of the motor is a crucial factor, for the following characteris-
tics:
• access to complex design, permitting adjustment of the internal ballistics;
• decrease of the inert mass in the motor;
• reliability and safety of operation;
• wide range of firing temperatures;
• industrial costs.
In the end, it turns out that for the reasons previously mentioned, the
development of insulation materials is one of the most difficult and time-
consuming of the tasks involved in the development of solid rocket motors.
582
Jean-Michel Tauzia
Here more than in any other area, it may be true that the predominantly
experimental nature of the techniques used must rest on the best-known
theories and a very rigorous experimental research, while leaving a large
place to the intuition and the experience of the designers.
Bibliography
1. BarrEre, M., and Jaumotte, A., La propulsion par fusee. Paris: Dunod, 1957.
2. Propellants manufacture , hazards and testing. Advances in chemistry series no. 88. Wash-
ington: American Chemical Society, 1969.
3. Schultz, R., Actes du colloque “Adhesion". Universite de Bordeaux I. Universite du Haut-
Rhin, France, 1979.
4. Kaeble, M., Physical Chemistry of Adhesion. North American Rockwell Corporation —
Science center, Thousand Oaks, California; Van Nostrand, 1967.
5. Sutton, G. W., The initial development of ablation heat protection: a historical perspective.
Journal of Spacecraft and Rockets , 19(1), 3-11.
6. Schmitt, D. L., Ablative polymers in space technology. Journal of the Macromolecular
Chemical Society, 13(C3), 326, 1969.
7. Lacaze, H., La protection thermique par ablation. Doc. Air Espace, nos. 105, 106 and 107,
July-Sept.-Nov. 1967.
8. Youren, J. W., Ablation mechanism for elastomeric rocket motor case insulation. Compo-
sites, no. 2, pp. 180-184, 1971.
9. Evans, C. I., Minimum smoke solid propellants rocket motors. AIAA paper no. 72-1192,
New Orleans, 1972.
10. Gonthier, B., and Tauzia, J. M., Minimum smoke rocket motor with silicones inhibitors.
AIAA paper no. 84-1418, Cincinnati, 1984.
11. Probster, M., and Schucker, R. M., Ballistics anomalies in solid rocket motors due to
migration effects. Acta Astronotica , 13(10), 599-605, 1986.
12. Gontheir, B., Maucourt, J., and Tauzia, J. M., Burning rate enhancement phenomena in
end-burning solid propellant grains. AIAA paper no. 85-1435, Monterey, California, 1985.
13. Graham, H., and Shepard, G., Composition et procede pour regler la vitesse de durcisse-
ment des resines polyurethannes. Thiokol corporation USA. Brevet frangais no. 2.386-570,
1977.
14. Bats, J. P., Lalande, R., and Tauzia, J. M., Systemes catalytiques retardes pour elastomeres
polyurethannes. Application a la preparation d ’inhibiteurs de combustion de blocs de
propergols. European Polymer Journal , 20(10), 997-1001, 1984.
15. Davis, R. T., and Bird, J. D., Reduction in cost of rocket motors manufactured by use of
liners with controlled cure. JANNAF propulsion meeting, Vol. V, pp. 435-465, Monterey,
California, 1980.
16. Tauzia, J. M., Elaboration d’adhesifs bicomposants sur le site d’utilisation. Fiabilite et
qualite des assemblages. Actes du congres Adhecom . Universite de Bordeaux, France, 1986.
17. Dessuge, P. H., Automatisation d’une installation de dosage bicomposants. Memoire du
Conservatoire National des Arts et Metiers. Centre de Bordeaux, France, 1987.
18. Schaffling, O., Process for preparing a rocket motor. OLIN corporation, US patent no.
4-131.051, December 1978.
19. Kirk-Othmer, H., Encylopedia of Chemical Technology. New York: John Wiley and Sons
1967.
20. Delacarte, J., and Quenu, P., Inhibiteurs a base de polyesters insatures. SNPE. Brevet
frangais, no. 1.194.649, 1959.
21. Caire-Maurisier, M., and Tranchant, J., Inhibiteurs halogenes pour propergols homo-
genes. SNPE. Brevent frangais no. 223.7117, 1975.
22. Lefort, M., and Brisson, P., Les silicones: synthese, proprietes et applications. Actualite
chimique, no. 8, 7-11, 1983.
23. Carter, R. E., and Wright, J., Procede de preparation de polyurethannes destines a revetir
une charge de propergol pour en inhiber la combustion peripherique et polymere et charges
revetus ainsi obtenus. Brevet frangais no. 2.444.689, 1979.
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583
24. Tauzia, J. M., Gonthier, B., and Grignon, J., Nouveaux inhibiteurs de combustion a base
d’elastomeres polyurethannes oxygenes comportant des fibres. SNPE. Brevet fran^ais no.
2.538.578, 1982.
25. Maucourt, J., and Combette, C., Inhibiteur preforme pour propergol composite a liant
polyurethanne. SNPE. Brevet fran^ais no. 8.610.820, 1986.
26. Tauzia, J. M., and Zilioli, F., Revetement inhibiteur pour propergol solide a combustion
frontale comportant des charges organiques. SNPE. Brevet frangais no. 2.495.133, 1980.
27. Case bonding composite for double-base propellants, US patent no. 3.960.088, 1976.
28. Klager, K., Polyurethanes, the most versatile binders for solid rocket propellants, AIAA
paper no. 84-1239, Cincinnati, 1984.
29. Sutton, E. S., From polysulfides to CTPB binders. A major transition in solid propellant
binder chemistry. AIAA paper no. 84-1236, Cincinnati, 1984.
30. Byrd, J. D., Consideration on the binding of large rocket motors. AIAA paper no. 76-638,
1976.
31. Gonzales, F., and Marks, F., Concept analysis for a low cost four-inch advanced tactical
rocket. AIAA/SAE, 13th Propulsion Conference, AIAA paper no. 77-868, Orlando, Florida,
1977.
32. Day, J. M., and Hortz, W. A., Nitrile butadiene rubber in ablative applications. Applied
Polymers Symposium no. 25, pp. 261-274, 1974.
33. Tauzia, J. M., and Maucourt, J., Protection thermique pour propulseur a poudre exempte
d’amiante. SNPE. Brevet fran^ais no. 2.458.687, 1979.
34. Doc Fiberite. Fiberite corporation Europe; ICI, PO Box 6, Bessemen Road, Welwyn Garden
City. Hertfordshire, UK.
35. Cazin, P. H., Les statoreacteurs a combustion liquide. Onera-Agard lecture, series no. 186,
1984.
36. Butls, P. G., and Myers, T. D., Integral booster motor interface requirements, AIAA paper
no. 78.160, Las Vegas, 1978.
37. Dvornic, P. R., and Lentz, R. W., Exactly alternating silirylene siloxane polymers.
Polymers, 24, 763-768, 1983.
CHAPTER 14
Future of Solid Rocket
Propulsion
ALAIN DAVENAS
1. Increase of Solid Propellant Energy
The progress made in the energetic characteristics of solid propellants
during the 1950s and the 1960s was followed by a period of disillusionment.
As with all new technology, the initial progress had- been very rapid. It
resulted from an excellent synergy between the needs related to applications
and the emergence on the market of chemicals supplied by the chemical
industry, well suited for the formulation of binders for solid propellants:
PVC, polyurethane, followed by more specific products such as various kinds
of liquid functional polybutadienes. This led to the creation of today’s typical
composite propellant, associating a polybutadiene binder with excellent
mechanical characteristics in a very wide range of temperatures to a high
content of oxidizers and fuels: ammonium perchlorate and aluminum
respectively. This is a particularly stable system, and involves a reasonably
easy production process in facilities where, aside from a few specific produc-
tion phases, the only hazard of concern is that of fire. Consequently, this type
of composition has progressively spread to a great number of applications,
such as missiles, rockets, and gas generators. For these applications the
immediate availability, long service life and good performance represent
major advantages, at least where the dimensions of the motor are not too
limited by space constraints, such as in the case of strategic missiles on
submarines, portable ground-air systems, or integral boosters on ramjets.
The research work done during the 1960s encountered great difficulties in
the synthesis and production of new molecules designed to increase the
energy of these propellants.
A great number of oxidizers more powerful and denser than ammonium
perchlorate were synthesized, tested and abandoned because of a high
chemical reactivity or a lack of stability (N0 2 C10 4 , for example) made them
incompatible with the existing binders, or because of high sensitivity to shock
or friction for industrial production (hydrazine mono or diperchlorate, for
example).
585
586
Alain Davenas
Techniques were subsequently developed to improve the compatibility of
energetic solid oxidizers included in the propellant: surface modifications
and, in particular, encapsulation of the particles by organic polymers
insoluble in the binder and compatible with the rest of the composition.
These techniques resulted in a decrease of the energy gain expected from the
formulation, and a significant cost increase for the preparation of the
propellant, but they may conceivably be used again in the future.
Many failures were also experienced with metallic fuels. Metallic hydrides
either exhibited densities that were too low to be interesting when the
hydrides were stable (LiH, LiAlH 4 ), or they were not stable unless complexed
with an organic molecule, thereby losing a good deal of their advantage
(A1H 3 , BeH 2 ). Extensive research has been done during the 1960s, in the
United States as well as in France and probably in the USSR, on composite
propellants containing beryllium. The reason for this is that the addition of
this metal significantly increases the specific impulse, without creating any
problems of compatibility with the hydrocarbon binders or ammonium
perchlorate. These developments were virtually abandoned because of the
very high toxicity of beryllium and particularly of its oxide resulting from
combustion, although there are controversies concerning the real toxicity of
oxide formed at the very high temperature of combustion in the motor. This
approach appears closed for the moment, although the possibility of starting
the research again comes up periodically, particularly for space applications.
There is one metal, however, that could have a definite future in some
applications, and in particular for tactical missiles of smaller sizes, such as
ramjet boosters. This is zirconium, with its very high density (6.49), resulting
in propellant with a volumetric specific impulse clearly above that of the
conventional polybutadiene-AP-Al propellant.
The thermochemistry and energetics of these various compositions are
particularly well described in the work from Boisson [1] which, although not
recent, continues to be recommended as a reference.
In the end, there seem to be two approaches open for the future: one is the
use of nitrated or nitro derivatives; the other, in the distant future, may be the
use of molecules containing fluorine not highly chemically bound in radicals
of the NF 2 type.
Among today’s most widely used energetic compounds, special attention
has been given to HMX which, in spite of its highly explosive nature, exhibits
high density, energy and stability. Two applications are: (1) the development
of specific polybutadiene-AP-Al formulations with some percentages of
HMX (12-20%); (2) XLDB type of formulation whose energetic binder,
more highly oxygenated, provides a higher specific impulse due to a possible
high content of HMX. These two types of compositions are being applied
either in apogee motors for space launchers (American PAM D 2 , for
example), or in advanced ballistic missiles for space launchers: Trident 1 C4,
Trident 2 D5, the third stage of the MX, and Midgetman in the United States.
Future of Solid Rocket Propulsion
587
Research continues in many countries on energetic solids or binders, or on
nitrated plasticizers that are more energetic or stable than binders with a very
high content of nitroglycerine. Molecules such as hexanitrohexa aza adaman-
tane or wurtzitane are the object of intensive research.
The avenue of the difluoraminated-type binders and oxidizers, which was
pursued because of the potential of very high specific impulse and density,
continues to be a highly difficult area of research direction. It seems to be
particularly oriented toward gem-difluoraminate molecules which preferably
include the geminal C(NF 2 ) 2 rather than the vicinal CHNF 2 , which is
unstable. This chemistry, which uses the difluoramine NF 2 H as a starting
material, is a difficult chemistry and it is very expensive.
However, an outside candidate has emerged that leads us to believe that in
the very near future we will be able to increase the energetic levels of today’s
propellants. It has been discovered in the United States that aliphatic
molecules containing the azide entity, N 3 , are stable and not very sensitive to
shock or friction. One particular polymer is presently under development, the
glycidyl azide polymer (GAP) [2].
Table 1 summarizes the main chemical features that are involved in the
research on new energetic compounds with high heat of formation and high
heat of combustion.
In the end there seems to be a definite trend again toward the research of
higher energies, which will be discussed in the next section. This has occurred
after a period during which research budgets for the improvement of
thermodynamic characteristics were drastically cut because of the disap-
pointments encountered in the chemistry of high energy materials. These
disappointments result in a great diversification of the more conventional
compositions in terms of their applications, which we will also discuss later.
Table 1 High energy groups
Group
AH/
(kcal/mole)
Use
— c— o— no 2
-19.4
plasticizers
— c— no 2
-15.8
solids
polymers
plasticizers
— N— NO z
17.8
solids
plasticizers
— c— n 3
80
plasticizers
polymers
— c— nf 2
— 7.8
solids
plasticizers
polymers
588 Alain Davenas
2. Propulsion of Strategic Missiles
The search for optimal propellant performance — specific impulse 7 S and
volumetric specific impulse 7 S p — will continue to be the most important
research mission, coupled with other expected technological progress which
will improve the propellant mass fraction (composite cases with very high
specific resistance, nozzle materials, and thermal protection) and with the
miniaturization of the nuclear warheads. These energetic gains will provide
the flexibility of design and usage corresponding to the various constraints of
the missions. It will involve, for example:
• For a missile of a given size (missiles on board submarines), increasing the
range or the number of warheads, countermeasures (decoys), or the
number of potential targets.
• A miniaturization of strategic missiles (the Midgetman concept in the
United States, project SX in France) to facilitate their transport and their
utilization, while at the same time deceasing their cost, allowing a
corresponding increase in the number of missiles.
• The evolution of past performances and those possible in the future is
illustrated in Table 2, which shows the improvement in performance of
propellants (in terms of the volumetric impulse 7 S ) over the years, based
on the American missiles until 1984, and then extrapolating from today’s
state of the art (propellants existing but not yet manufactured indus-
trially). The source for this table is a paper written by D. Quentin [3], to
which we will refer to a number of times in the following sections.
Table 2 Past and predicted evolution of solid propellants for strategic missiles
Formulation
Theoretical / s
standard
conditions
P
g/cm 3
h.p
Estimated
date of
completion
of
industrial
development
Butalane 68/20
265
1.815
481
1968
Nitralane Trident C4
271
1.84
498
1973
Nitralane Trident C5
273
1.87
510
1978
FI
276
1.89
522
1985
F2
280
1.91
535
1995
F3
296
1.91
565
2010
Note: The performances assigned to the future formulations (FI, F2 and F3) are the results of
calculations, and consequently involve a certain amount of uncertainty concerning the
possibility of attaining them in practice.
The dates correspond to the demonstration of the industrial feasibility of the propellants
rather than their introduction in a missile program.
FI and F2 compositions are based on nitrated or azide ingredients.
F3 composition contains difluoraminated derivatives.
Future of Solid Rocket Propulsion 589
Based on these elements, we see that, taking only thermodynamics into
account, there is a considerable potential for improvement.
However, we should point out that these propellants, in comparison with
the conventional composite propellants, present the same drawbacks as those
experienced with high-energy XLDB propellants: (1) small critical diameter;
(2) manufacturing involving delicate phases because of the use of large
amounts of explosive ingredients. Solving the latter requires high invest-
ments, and thorough knowledge and control of the deflagration-detonation
transition phenomenon. The approach taken in the United States with the
ballistic missiles of the Trident and MX family shows, however, that these
various aspects can be handled, resulting in reliable, high-performance
systems.
Before they can be produced, these future propellants will also need to have
sufficient mechanical properties allowing them to be case-bonded, and aging
properties that are compatible with the typical service life of the ballistic
missiles motors, i.e. at least 10 years.
The architecture of the grains, based on the levels attained today (loading
ratio greater than 95%), should not evolve noticeably if the architecture of
the motor remains the same (we will discuss the concept of integrated stages
further).
Another general possible evolution is related to the hardening of the main
stages of the missiles against space-based lasers that could be used in the SDI
concept. This hardening could involve rotation of the missile and much lower
burn times of the stages, phases during which it is the most sensitive. So high-
rate, high-energy propellants would be considered.
Special propulsion systems need to be contemplated for the post-boost
control systems which require special solid propellants. The best propellant
energy management in these systems implies the availability of solid propel-
lant with modulable flow rates or the availability of extinguishable and re-
ignitable (start-stop) systems.
The future trends seem to be as follows: for ground-based missiles with a
large number of warheads to deliver we are experiencing a return to liquid
propellants systems. This is due to the fact that they allow a greater amount
of flexibility in adjusting the thrust, and easy control of the extinction and re-
ignition of the motor, with very high specific impulses.
In the case of systems on board submarines, the liquid propellants are less
acceptable (risks of leaks from the tanks, corrosion, limited space available,
and low density of the propellants). Two types of systems are possible for
present and next future systems. The classical post boost system used on
missiles of the Poseidon and Trident family, which uses propellant gases
produced by a generator modulated by a valve. At the technical level this
implies the availability of the propellant with low burning rates (the
operational times must last several minutes) and the highest possible specific
impulse, while not exceeding gas temperatures acceptable for the valves and
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Alain Davenas
the pipes of the system. In the United States the materials used are generally
Colombium alloys, which limit the temperatures to approximately 1900 K. In
France extensive work is being done with carbon-carbon composite mater-
ials allowing temperatures up to 2400-2500 K, and consequently, higher
specific impulses. Butamites or nitramites, with “cold” nitrated binder and
high HMX content, are propellants well suited for this type of need. Another
characteristic of these types of systems is the need for very clean combustion
gases, to avoid clogging of valves and pipes. Mineral compounds are
generally not used in the composition of the propellant; as for inhibitors and
the thermal protection of the chamber, gasifiable formulations, also used in
low-signature tactical missiles, are preferable.
With the throttlable or controllable system, with separate solid propel-
lants, the main motor functions only when a gas generator — with low
combustion rate — generates flows inside the combustion chamber. When
the gas injection is interrupted the main grain extinguishes. The correspond-
ing propellant compositions are often fairly reducing for the generator, and
oxygenated for the main grain. High specific impulses, associated with an
operation that includes more than ten thrust pulses separated by motor
extinction phases of varying duration, have been demonstrated in France.
A concept studied by Aerojet [4] is similar to this system. It features two
solid propellant generators: one for oxidizing gases and the other for the
reducing gases. Their flow rates are independently adjustable; they both flow
into one single combustion chamber.
We should also mention that in the area of general architecture for multi-
stage ballistic missiles, an interest is developing in an integrated stage
concept, whereby the front end of the lower stage forms the exit cone for the
nozzle of the next higher stage. This concept would lead to a 20% increase in
range. A “forced deflection” nozzle, using a special boron-based propellant,
has been demonstrated in the United States in a chamber simulating high-
altitude conditions [5]. A related system, though less ambitious in terms of
the innovations involved, has been recently demonstrated [6].
Finally, we should also note, in relation to the development of solid
propellant boosters for space launchers, the trend of manufacturing facilities
toward the processing of very large quantities of composite propellants in one
manufacturing operation, still using the batch process. The unit operation
has grown from 2-3 tons to approximately 15 tons. Today, modern automa-
tion technology results indicate significant drops in manufacturing costs.
For the longer-term continuous processes, presenting revolutionary possi-
bilities are being developed and will be addressed in the section on space
boosters.
3. Propellants for Tactical Missiles
Each mission has its own specifications and requirements, as illustrated in
Table 3. Although this presentation is largely arbitrary — for instance no
Future of Solid Rocket Propulsion 591
Table 3 Characteristics of solid propellants for tactical missiles as a function of their
missions
Types of Missiles
i,p
Signature
Temperature
coefficient
Duration of
combustion
Artillery rockets
X
X X
Anti-tank
Rockets
XXX
X X
very short
SR
X
XXX
X X
M and LR
X X
XXX
X X
Ground air
VSR
MR
X
X X
X X
X X
X X
LR
X X
X X
X X
long
Air-ground
Rockets
X
X
X X
Missiles
X X
X
X X
long*
Air-air
SR
X X
X
X X
MR
X X
X
X X
Sea-sea
X X
XXX
X
long*
Note: x , not an important criterion; x x , of average importance; x x x , highly important.
SR = short range; MR - medium range; LR = long range; VSR = very short range.
missile manufacturer believes that the cost of the propellant is marginally
important — it still allows us to identify the trends. Naturally, the service life
and storage and operational safety are also included in the main specifica-
tions.
Before getting to the solutions (propellants, grain geometry) for these
problems, it would be interesting to take a closer look at the evolution of
some specifications.
3.1. EVOLUTION OF THE NEED
3 . 1 . 1 . Signature and penetration
The lowering of the electromagnetic, infrared, and optical signatures of
missiles is intended above all to delay the use of countermeasures. In fact, a
low signature is one of the means of ensuring the superiority of the attack
over defense, so that future missiles will retain their capability of penetration.
Extensive efforts are devoted to reducing the visible, infrared, and electro-
magnetic signatures. A reduction of the electromagnetic signature — charac-
terized by the radar cross-section — is obtained mostly by changing the
architecture or the materials: limiting “bright spots”, using coatings that
absorb or diffuse radar waves and special shapes, which could lead to missiles
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Alain Davenas
with elliptical or triangular sections. This in turn would result in completely
new problems in terms of the propellant grain.
We will not discuss decoy systems, although we will comment briefly on
the maneuvering capability the manufacturers would like to provide their
missiles in order to outwit the defense systems. In terms of propulsion, such a
capability would imply several indispensable attributes, including: (1) the
modulation of the thrust which may lead, even for a missile, to three or even
four successive thrust levels which, of course, becomes extremely problematic
for a single grain; (2) the capability of the grain to withstand acceleration
factors.
3. 1.2 . Environment
The number and severity of constraints under which future missiles will be
used are continually increasing, particularly in terms of the extreme tempera-
tures of operation and storage. In the course of the last 30 years these have
progressed from propellants usable in a - 30°C to + 50°C temperature range
to propellants with a working range from -54°C to + 70°C, and able to
resist to peaks reaching temperatures close to 100°C. This corresponds, in
particular, to the extension of the flight domains (altitude and speed) of
aircraft, for air-launched missiles.
These constraints present the grain designers with two critical problems.
Not only is it necessary to maintain the mechanical and physical integrity of
the grain within the operational ranges, and its reliability after severe thermal
cycles — consequently requiring excellent mechanical properties at all tem-
peratures — but it is also necessary to maintain the performance (thrust,
pressure versus time) in the same range (reduction of temperature coefficient).
The problems linked to the temperature ranges involve several other
parameters, including:
• the intrinsic mechanical properties of the propellant;
• the geometry of the grain;
• the grain-case interaction, related to deformation under pressure from
the case and to its thermal expansion characteristics.
This last point is an important one. Indeed, the evolution toward increasingly
thinner metallic cases, made feasible by flow-turning processes and the use of
filament-wound cases (Kevlar and carbon fibers), modifies considerably the
behavior of the motors in terms of deformations under pressure (to which are
added the difficulties of calculation and local anisotropies). It also modifies
the need to take into account the whole composite propellant-case to
calculate the stresses and strains which determine the safety coefficient and
the service life of the motor.
Naturally, the improvement of the mechanical characteristics of the
propellant give the grain designer a greater amount of flexibility in his search
Future of Solid Rocket Propulsion
593
for a solution. In addition, the generalization of the three-dimensional
analyses validated through experiments, and the use of more sophisticated
rheological models, improve the reliability of the predictions and the estima-
tion of the service life.
3 . 1.3. Maneuverability; thrust modulation
We mentioned, when discussing the signature, the necessity for maneuvera-
bility on part or all of the trajectory to defend against anti-missile weapons.
Without a doubt the next generation of air-sea or sea-sea missiles will feature
a supersonic final path to foil the enemy defenses. Conversely, anti-missile
missiles design will have to be able to react almost instantly, to maneuver
with agility once the target has been detected.
3.1.4. Increase range
For air-ground, air-sea, and sea-sea missiles the possibilities of detection
or identification of remote targets and the desire to escape from enemy
defenses (such as launching aircraft or battleship) requires significant in-
creases in missiles range, which, as we will discuss later, demonstrates the
value of the air-breathing type of solutions.
3.1.5. Vulnerability
Low vulnerability specifications of the type described in Chapter 8 will
certainly be imposed for all missiles. In the United States the objective, a very
ambitious one, is to use missiles meeting “insensitive munition” requirements
by 1998.
3.2. EVOLUTION OF THE TACTICAL PROPULSION
3.2.1. Propellants
Propellants are generally classified into three families:
• double-base (extruded or cast);
• composite with inert binder;
• composite modified double-base with energetic binders, CMDB or
XLDB type.
The first two families — also the oldest — will continue to develop in two
major directions: increase of burning rate ranges, and development of low-
cost processes for industrial production.
The third family will be affected by the application of high-energy, low-
signature propellants and their development within the framework of low
vulnerability specifications.
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Alain Davenas
The expected improvement, over the years, of the performance of the low-
signature propellants for tactical missiles (/ s .p) is illustrated in Table 4.
One of the major difficulties encountered with the newer types of smokeless
high-energy propellants is the present limitations in rates of combustion
available. This is certainly one of the main subjects for research in the near
future.
3.2.2 . Grains for thrust modulations
There are already many grains that have two thrust rates and thrust ratios
capable of reaching factors of 7 to 8. These rates, however, are currently
predetermined, while the missile designers wish to be able to trigger an
“overrate” on request, as a function of the proximity of the target. Designs
with complex geometries — with an increase of the burning surface at the
desired moment — are being developed and are expected to be operational
within the next few years, particularly for applications on the new sea-sea,
air-surface, or air-air missiles [7,8].
3.2.3. Increase range: air-breathing systems
With air-ground and sea-sea missiles, and sometimes also ground-air, the
ranges are limited by the weight of the missile, and also by the burn time
available for the sustainer grains (more than 150 s is now available).
A simple solution, in principle, consists in using the air-breathing propul-
sion. There are several alternative development paths: turbojet, ramjet and
ramrocket, and in the longer term, air turboramjet and turboramjet.
The adaptation of aircraft turbojets by simplification of the compressor,
and of the lubrication and injection systems, and the use of low-cost materials
Table 4 Past and potential development low-signature solid propellants for tactical
missiles
Formulation
Theoretical l s
standard
conditions
Density p
g/cm 3
i,p
Estimated
date of
industrial
development
EDB — CDB
229
1.66
380
1970
CMDB
241
1.67
403
1982
XLDB
256
1.76
450
1985
FI
259
1.77
458
1988
F2
261
1.81
472
1993
F3
262
1.83
479
2000
Note; All of these formulations correspond to basic compositions of the CHON type — mix-
tures of ingredients containing only these atoms — possibly with the addition of low amounts
of ballistics modifiers.
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Future of Solid Rocket Propulsion
for application where the operational time is limited to several hours, makes
this propulsion system competitive with the rocket motors. Currently they
are limited, however, to subsonic and slightly supersonic flights.
The technology of the ramjets and ramrockets is ready for numerous
applications to missiles. The systems now developed actually reach ranges of
several hundred kilometers [9], and ranges of several thousand kilometers
are a possibility being investigated. The development of this type of propul-
sion is going to take several directions. The integral boosters (in the
combustion chamber of the ramjet) without ejectable nozzles (for launching
from aircraft in particular) will become widely used on combat platforms,
implying such related problems as: design of nozzleless grains, prediction of
the performance, and precise thrust vector control. The bonding and thermal
protection materials of the combustion chamber will have to be capable of
two functions: booster function and very long-lasting ramjet function, for
which the temperatures and composition of the gaseous mixtures are very
different.
Because of volume and space limitations, the desired increase in range
requires the use of high-energy propellants or high volumetric impulse
propellant types for the booster phase, and dense liquid fuels or boron or
carbon solid fuel-rich propellants for the sustainer phase.
The search for simplicity in manufacture, if not in design, has led to the
creation of the experimental model known as the “rustique ramjet” where a
single chamber contains both the booster and the sustainer grains. This type
of ramrocket has been flight-tested several times in France [10].
The turboramjet is a newer design intended to operate as a turbojet at
subsonic speeds and as a ramjet at supersonic or hypersonic speeds. It
includes, briefly described: an air intake, a compressor, a turbine, a generator
of reducing gases, a combustion chamber, and a nozzle.
The air entering into the motor is compressed by the low-pressure
compressor, which is driven by a high-pressure turbine powered by the
reducing gases from the generator. The system is capable of accelerating up to
its cruising speed, without any additional boosters.
The major advantages of this design are: (1) better thrust and specific
impulse, as well as a more stable burning rate than in a ramjet alone; (2) a
turbine less complex than the conventional turbines; and (3) a better thrust/
weight ratio than with the ramjets.
Among possible applications there are stand-off supersonic missiles, cruise
missiles, air-ground missiles, and drones.
3.2.4. Low vulnerability propellants
This topic, particularly sensitive for missiles on board ships or on aircraft,
requires research into propellants with a low vulnerability to stimuli from
projectiles, fire, static electricity, and in addition possessing a pyrotechnical
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Alain Davenas
behavior preventing the combustion-to-detonation transition. It is likely
that, during the coming years, this theme of “low-vulnerability” propellants
will become very important. The most important question, still undecided to
this day, will be whether a trade-off with energy performances will be
tolerated. It is certain that it will be extremely difficult to significantly lower
the vulnerability while maintaining the high levels of performance obtained
today, although this is the goal of a large number of important research
programs [11,12].
Many of the ingredients being studied for an energy increase in today’s
propellants could also serve to decrease the vulnerability, for an equal level of
energy.
3.2.5 . Processes; decrease in costs
Decreasing costs is a permanent goal. It is sought both at the level of the
design of the grain, by performing value analysis in cooperation with the
missile manufacturer to satisfy the operational requirements, and at the level
of the manufacture:
• reduction of manufacturing cycles;
• automation of industrial production;
• integrated processing systems;
• selection of materials;
• highly economical, non-destructive quality control tests.
The large industrial production processes already being tested, involve:
• the use of continuous screw extruders: extruded double-base and compo-
site propellants with thermoplastic binders but also now with thermoset-
ting binders;
• the implementation of high production rates, short cycles, and inhibiting
techniques;
• high rate of injection systems for composite propellants, and reduction of
the cure cycles.
For composite propellants, revolutionary progress (costs decreased by more
than half) will be obtained only through extensive modifications of the active
parts of the manufacturing process, such as continuous mixing. So far, the
difficulties facing this development do not involve basic issues such as
mechanical components, but rather the amount of precision required in the
continuous feeding of raw materials, and the high level of sensitivity of the
propellants to minute variations in the amounts of crosslinking agent, or
catalyst. Therefore, progress should come from improvements in the preci-
sion of the feeding control equipment, and from the modification of the
compositions to render them less sensitive in this area.
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Future of Solid Rocket Propulsion
4. Propulsion of Shells
An area related to that of tactical missiles, where we will see the use of
propellants and semi-propellants increase during the coming years, is the
area of projectiles launched from a gun. Increasing the range of ballistic
artillery projectiles, and increasing their velocity on the flat trajectory are
constant goals.
Beyond the range increase through reduction of the base drag discussed in
Chapter 10, research efforts are focusing on air-breathing propelled shells.
The major problem consists in placing and having a ramrocket function
inside a projectile launched from a gun, and often spin-stabilized. For these,
the range of a 155 mm projectile could be increased to 50 km. In the case of a
projectile stabilized by tail fins, ranges of 70 km are being predicted. Tubular
projectiles, with a kinetic effect resulting from an air-breathing propulsion,
are also being studied for anti-tank applications.
At any rate, all solid fuels to be used will have to produce combustible
gases capable of burning efficiently in combustion chambers very limited in
their lengths. The nature of these solid fuels and the design of these grains will
have to overcome problems associated with a gun environment: very high
pressures, high initial axial and radial accelerations, and rapid drop of
pressure — for instance, when exiting the gun — while ensuring a consistent
performance.
5. Space Launchers and Space Motors
This area is one where solid propellants are not doing as well as liquid
propellants. All of the following factors have led to a wide use of liquid-fuel
rocket engines on heavy launchers: (1) higher levels of specific impulse, and
the possibility of easily modulating the thrust; (2) the ability to feed the
propellant tanks at the last minute, unlike military missiles, thereby allowing
the use of propellants not suitable for long-term storage; (3) less strict
volume/weight limitations. Solid propellant rocket motors (Diamant A or B
in France, from 1964 to 1972, and the first Japanese launchers, Scout in the
USA) were used at the beginning of the space era, either because they were
directly derived from the military technology of ballistic missiles, or because
the payload was fairly small.
Solid propellant grains continued to be used in two types of motors related
to the development of space applications: additional boosters for take-off,
allowing an increase in the payload of a liquid propellant launcher (Ariane 3
and 4, for example), and the perigee and apogee motors designed to place
satellites on geostationary transfer orbits from parking orbits.
Many motors of this type have been developed in Europe (motors for the
MAGE family) or in the United States (STAR family), some of them
attaining large dimensions, such as the Inertial Upper Stage SRM-2.
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Alain Davenas
With the American space shuttle emerged an architecture already tested on
the Titan III launcher, whereby the whole is designed in such a way that the
central liquid propellant motor is not capable of ensuring take-off of the
system by itself. At that point, 80 % of the thrust is provided by the boosters of
the space shuttle. This type of launcher architecture, which utilizes solid
propellant grains that are gigantic in comparison with what is used on the
larger stages of military ballistics missiles, could become widely developed
because the same type of architecture is being considered for the future
European Ariane 5 launcher and for the future Japanese heavy launcher
(HII).
The mass of propellants involved in these motors (several hundreds of
tons) prevented in the past the production of monolithic grains. These grains
are consequently case-bonded, and made of segments manufactured separa-
tely and later assembled. The propellants used, for reasons of safety and cost
are generally polybutadiene-AP-Al propellants.
The progressive use of space for military purposes may confirm this trend
toward solid propellant motors: the Department of Defense of the United
States defines the main objectives that must be reached by the technologies to
be used in the future military space systems as follows:
• immediate availability,
• low vulnerability,
• affordable cost,
• simplified logistics,
• reliability.
These are the very characteristics that have guaranteed the success of the
solid propellant motors used on the strategic missiles, leading in the past to a
success rate over 90% for American military satellites launched by solid
propellant launchers. To this, we may add that, for the very high mass flow
rates considered, solid propellants give efficient and easy solutions and that
the costs of development and production of solid boosters are lower than
with liquids. MacDonald [14] has done a very detailed study of the various
possibilities of development of these solid propellant space systems, using
either existing motor assemblies, in particular the boosters of the shuttle, or
improved-technology motors, focusing in particular on their competitiveness
with the liquid fuel engines. More recently the AIAA Solid Rocket Technical
Committee has emphasized [15] the potentials of solid rocket motors in the
frame of US studies on a future ALS (advanced launch system). The stringent
requirements for improvement of cost and reliability related to these applica-
tions, and perhaps environmental considerations, may lead to dramatic
evolutions of this technology [16].
The present technology used on space boosters is a 20-30-year-old
technology based on previous experience in tactical or strategic missile
systems. In its most advanced form the propellant used is a composite
Future of Solid Rocket Propulsion
599
propellant: polybutadiene (HTPB), AP, A1 with 86-88 % solids. This is a low-
cost binder with a very good processability; it has a very attractive curing
system which gives to the propellant a long pot-life and short cure times and a
low viscosity enabling easy casting and high quality. The reliability of the
cured propellant grains is good: good mechanical properties are achieved,
good liners giving good bonding are available. There is an important
experience with tactical and ballistic systems using this type of propellant. It
will be used in the Ariane 5 boosters, HII boosters. Titan IV boosters and
ASRM for the shuttle.
The processing facilities use batch mixing for the propellant and the
nondestructive testing inspection is done with radiographic static controls
with a progressive evolution toward automatic dynamic inspection using
computer-aided radioscopy or tomodensitometry for exploration of the
whole grain.
In their most advanced form these facilities represented by Bacchus West
Hercules facility or the facility that is being built in Kourou (French Guyana)
for the Ariane 5 boosters have the following characteristics:
• Specialization in the case of the Kourou facility; it is designed to
manufacture only the main (100-ton) segments of the booster. This
facility is close to the launch pad, enabling minimum handling.
• High level of automatization and computer on-line data acquisition and
control.
• Batch processing, using for cost the highest capacity available mixer
(1800 gallons, 13 tons of propellant per mix).
For the future continuous mixing is being considered.
Like any transformation industry the solid propellants industry has
considered very early [17] the use of continuous processes that would
be — compared to the batch processes — more economically efficient and
safer, since a smaller quantity of propellant is worked on at a given time. The
competition between increased size of the batch mixers and the continuous
mixers has been favorable to the batch mixers in the past 30 years, even if
Aerojet had operated a continuous mixing facility in the sixties [18].
The situation is changing since Aerojet will use a continuous process [19]
for the new improved boosters for the shuttle (ASRM).
The main technical problems involved in continuous mixing have been
described in Chapter 10. They are mostly related to precise continuous
metering of the raw ingredients and to continuous in-line chemical control of
the propellant. A Polybutadiene-AP-Al propellant will still be used.
Other more exotic processes are being researched, but are far less advanced
so that their future is unpredictable. Some of them could use thermoplastic
elastomers as binder for the propellant; no curing would be needed. A process
called MEGABAR uses as oxidizers ammonium nitrate-based eutectic
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oxidizers which are liquids during the mixing operation, which thus becomes
easy and very rapid.
Besides the evolutions that originate because of the work on process
improvement some research is devoted to clean or non-polluting propellants
[16,20,21].
The AP propellants generate a very high level of hydrochloric gas and
aluminum oxide, typically more than 20% of HC1 and about 35% of A1 2 0 3
can be found in the exhaust gases of our HTPB, AP, A1 reference propellant.
The simple solution to the problem is to use an HC1 scavenger like KN0 3
or NaN0 3 . HC1 will be replaced by KC1 or NaCl in the exhausts. The penalty
on specific impulse — a loss of 15-20 s — will be severe. The use of NH 4 N0 3
instead of AP would also lead to a severe performance loss. This could be
compensated by using an energetic binder — and since in that application we
do not want a too-sensitive one — quite a lot of work is devoted to GAP-
TMETN binder.
5.1. MONOLITHIC GRAINS FOR SPACE BOOSTERS
The monolithic (non-segmented) boosters could have greater simplicity
and reliability, and may have some advantages for cost. The main problems
encountered would be [22]:
• the size of the molding tools and mandrels (they could be segmented,
etc.);
• the casting of the propellant;
• the handling of these gigantic assemblies (we could imagine that all the
operations would be done with the case in the same position until the
final assembly, etc.);
• safety problems involved with such big masses of propellant;
• the size of the nondestructive inspection systems;
• the overall cost of demonstrating the validity of the concept.
Other avenues of technological evolution seem to have been opened by the
Strategic Defense Initiative (SDI) of President Reagan toward either counter-
measures by the “hardening” of strategic missiles and re-entry vehicles, which
should lead to a requirement of very high energy and very high burning rate
propellants (taking into account the increase in mass), or development of
propulsion systems of anti-satellite or anti-re-entry-vehicle missiles, with
conventional explosive warheads. The specifications for these systems are not
completely developed, although they will certainly lead to:
• Attempts to reduce costs to a minimum, based on the large numbers of
launches that may be involved for ground-based interceptors designed to
intercept in the high atmosphere or exoatmosphere, or for launching of a
large number of satellites at the last minute [23-25].
Future of Solid Rocket Propulsion 601
• Very high volumetric performance and special resistance to thermal
cycles for interceptors based on satellites.
6. Conclusions
In the final analysis it appears that, as in many cases, the technological
progress of propulsion systems using solid propellants is due at least as much
to the expression of new requirements and the emergence of diversified
applications, as to the results of basic research disconnected from any
requirement specifications.
We have seen that a potential for improvement of the characteristics of
solid propellants does exist, and that the development of these character-
istics — especially for diversified space applications and the replacement of
tactical missiles with newer, more versatile ones — should constitute an
important field of study.
The applications of propulsion systems using solid or liquid propellants
could also become more intertwined than in the past. We have seen, for
instance, the return to bipropellant systems for the upper stages of ballistic
missiles, while at the same time large solid propellant boosters were making a
breakthrough on space launchers. And while liquid propellants seem to be
useless for tactical missiles (with the exception of drone missiles and the
possibility of using liquid propellants in a gel form), there will be strong
competition for the middle- and long-range tactical missiles between the
liquid fuel ramjet, the solid propellant ramrocket, the turbojet and the
turboramjet.
Beyond applications to very high-performance military missiles, the em-
phasis will be placed on costs, particularly for mass industrial productions
and very large missiles (artillery rockets and space launchers). This emphasis
will not only be on production costs but also on development costs, implying
significant changes in the methods of development: systematization of the
approach by value analysis done at the pre-design phase; computer-aided
automatic methods for the design phase; overtests performed within the
framework of the development program, etc.
Finally, three new directions of effort have recently emerged that may have
significant consequences on the renewal of the family of solid propellants: low
vulnerability research, the various projects related to the American Strategic
Defense Initiative and the technology evolution of the new space boosters.
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Index
Ablation 105, 195, 554, 558, 559, 572, 575
Acceleration 42, 48, 49, 59, 139, 351, 550,
592
Acoustic balance 177, 186
Acoustic modes 65,173-175
Adhesion 554-558, 574, 576
Afterburning 199, 341, 400, 402, 511,513,
561
Aging 364, 365, 370, 408, 409, 432, 465,
517-519, 554, 561,562
Airbreathing motors 26, 106-109, 594, 595
Aluminum 5, 11, 42-46, 96, 126, 139, 357,
403, 438, 462, 488, 497, 498, 533, 551
Ammonium nitrate 416, 429, 437, 463, 466,
599
Ammonium perchlorate 42-46, 96, 125,
127, 197, 316, 341, 348, 357, 416, 428,
435, 460, 461, 462, 487, 490, 496, 498,
504, 509, 510, 517, 520, 534
Anisotropy 451-454
Antioxidant 432
Azide 483, 587, 588
Ballistic modifier 123, 128, 372, 376, 396,
408, 427-428, 488,513
Base bleed 349
Beryllium 438, 586
Binder 42, 46, 1 26, 1 30, 237, 4 1 5, 4 1 6, 4 1 7,
418, 430, 433, 440, 471, 479, 480, 505,
516, 530, 571, 576, 585
Blast tube 8
Bond 265-269, 454
Bonding 185, 215, 294, 417, 455, 494, 549,
554, 556, 562, 563, 564, 565, 567, 580
Bonding agent 430, 486, 555
Boron 357, 438, 533, 534, 537, 545, 549, 590
Burning area 55-57, 75, 100
Burning rate 10, 12, 13, 58, 61, 63, 82, 100,
111 117, 307, 334, 335, 351, 356, 375,
394, 395, 468, 488, 489, 506, 508
Burning rate accelerator 427
Burning rate enhancement 83, 136, 561, 562
Burning rate law 14, 59, 112, 128
Burning rate models 124, 129, 132
Burning rate moderator 428
Carbon-carbon 8
Card gap test 309, 312, 322, 412, 520, 521
Case 2-5, 50, 343, 344, 454, 472, 494, 549,
567, 568, 570, 592
Case bonded grain 5, 37, 79, 218, 280, 338,
343, 415, 417, 448, 453, 455, 478, 493,
500, 503, 549, 566, 567, 576
Casting 37, 383, 388, 416, 442-450, 453,
497, 502, 566
Casting powder 42, 371, 377, 383, 385, 387,
478, 490, 491. 492, 502, 520, 521
Casting solvent 383, 386, 387, 480, 502
Catalyst 431,442,486,571
Centrifugation 568
Char 554,558,574
Chemical stability 371, 404-408, 497, 515
Clean propellant 600
Combustion instability 64, 80, 81, 172, 373,
401-404, 513-515
Combustion mechanism 121, 124, 131
Combustion efficiency 26, 530, 537, 544,
548
Compatibility 376, 416, 434, 483, 554, 556,
562, 563, 586
Condensed phase 24, 85, 142
Conductive combustion 305, 307
Coning 41, 83
Continuous mixing 442, 596, 599
Convective combustion 305, 306, 308
Cook-off 218, 306, 317, 318, 347, 348, 41 1,
467, 471, 497
Cost 4, 42, 81, 343-345, 351, 361, 551, 553,
596, 598, 600, 601
Creep 243, 246
Crosslinking 4 1 6, 4 1 8, 423, 425, 464, 466,
480, 492, 496, 504, 505, 568, 574, 576
Crystallization 487, 499-500
Curing 4, 5, 220, 383, 388, 416, 431, 450,
464, 485, 496, 497, 506, 518, 522, 576,
599
603
604
Index
Damage 261, 288, 294, 453
Damping 179, 188, 376, 403, 514
Deflagration 305, 520
Deflagration to detonation
transition 309-31 1, 323, 520, 522, 589
Density 8, 10, 21, 332, 385, 386, 387, 391,
436, 490, 493, 497, 510, 531, 532, 533,
554, 572, 580, 594
Design to cost 362
Detonation 304, 306, 308, 314, 316, 346,
347,411,467, 469, 521
Detonation critical diameter 49, 308, 325,
347, 348,412, 469
Discharge coefficient 10, 1 1, 20, 89
Dynamic loads 297-300
End burning grains 40, 41, 83, 97, 383, 390,
548, 559
Equivalence ratio 534, 539, 545, 548
Erosive burning 52, 61-63, 75, 157-164, 404
Expansion ratio 7, 23, 55, 75, 89
Extrusion 42, 379, 383, 384
Failure criteria 71, 77, 257-261
Ferrocenic derivative 128, 427, 461,
468-471
Finocyl 40,137,156,175,453
Flash suppressor 210, 376, 400, 408, 513
Flow 15, 24, 31, 59, 86, 140, 153-157, 194
Flow rate 10, 1 1, 89, 335, 356, 534, 539, 544
Fluoramino compounds 587, 588
FMECA 76
Free standing grain 5, 37, 40, 222, 343, 500,
566, 575
Friction sensitivity 314, 3 15, 41 1, 470, 521,
522, 543
Fuel rich propellants 106, 527, 529, 532,
535, 538 545, 548
GAP 587
Gas generator 2, 106, 158, 350, 351-354,
460, 463, 528, 539, 545, 548, 590
Glass transition temperature 336, 421, 497,
498
Hazard division 320-324, 345, 522
Heat capacity 391
Heat of combustion 530, 532
Heat of explosion 386, 391, 398, 403, 407
Heat transfer 15, 159, 160, 168, 354
HMX 42-46, 125, 344, 437, 462, 487, 507,
586, 590
Hump effect 59, 136, 137, 451, 452
Igniter 354,355,356
Ignition 3, 4, 9, 42, 51, 63, 67, 75, 80,
167-172, 304, 314, 316, 317, 338, 351,
354, 356, 372, 379, 410, 469, 473, 537
Ignition delay 169
Ignition compositions 356-359
Impact sensitivity 313, 411, 543
Incompressible 67, 68, 250, 282-286
Infrared 201, 203, 208, 399
Inhibitor 380, 381, 553, 566, 570, 571, 590
Insensitive munitions 4, 345-347
Integral booster 81,526,549,579
Integral molding 450, 486, 497
Isocyanate 423, 485, 492, 496, 571, 574, 576
Klemmung (burning area to throat area
ratio) 11, 13, 14,75, 93, 185,323
Kneading 377, 378, 384
L* instabilities 173, 177
Labor regulations 320, 322
Liner 6, 38, 417, 454, 494, 550, 553, 567,
576, 578
Longitudinal instabilities 173, 181, 401
Loss 24,25,97,180
Mandrel 3, 4, 38, 443, 446, 449, 452, 567
Mass flow rate 1, 17, 19, 27, 48, 63, 75, 130
Mass flow rate response 175, 176
Mechanical behavior 66, 67, 227, 235, 239,
251, 274, 298, 336, 393, 502, 505, 522
Mechanical capability 66, 71, 77, 217, 268,
339, 341, 463, 464
Mechanical imbedment 569
Mechanical loads 35, 68, 70, 77, 218, 338,
416
Migration 427, 454, 466, 518, 562
Mixer 384, 441, 496, 599
Mixing 383, 384, 416, 439-442, 496, 568,
600
Molding 450
Monolithic boosters 600
Nitramine 125, 483, 487, 490, 496, 498, 510,
517, 520, 562
Nitrocellulose 42, 329, 370, 373, 377, 383,
384, 477, 481,504
Nitroglycerine 42, 329, 370, 374, 377, 383,
384, 386, 477, 483, 496, 499, 500, 587
Nitroguanidine 374, 429, 437, 461
Nondestructive inspection 364, 454-461,
565, 599, 600
Index
605
Nozzle 6-9, 15, 16, 17, 18, 27, 50, 51, 59, 75,
89, 92-94, 107, 180, 194, 344, 525, 526,
547, 549, 590
Nozzleless motors 81-82, 549, 550, 595
Operating pressure 7, 12, 22, 75, 102, 402
Optical transmission 95, 201, 206, 399,
559-561
Overtest 78
Oxamide 429, 575
Paste 378
Peeling 270, 563, 570
Plasticizer 37 1 , 375, 422, 425, 427, 479, 480,
481, 483, 495, 498, 499, 562, 571, 578
Plateau 372, 395, 396, 397, 507-508
Plume 48, 97, 193, 199, 204, 560
Poisson ratio 227, 229, 230, 283
Polybutadiene 45, 96, 417, 423, 427, 432,
461-462, 471, 474, 530, 534, 540, 576,
585, 598, 599
Polyester 421, 432, 462, 474, 481, 504, 510,
530, 571, 574
Polyether 421,460,481,510,574
Post boost control system 462, 589
Pot life 416,431,542,566,567,599
Preliminary design 3, 20, 21, 36, 52, 72-75
Pressure coupling 175, 178, 181
Pressure effect 249, 252-261
Pressure exponent 58, 112, 128, 396, 427,
463, 489, 510, 547, 550
Pressurization 70, 220, 223, 224
Primary smoke 196,211,341,512
Pyrolysis 41, 118, 554, 558, 561, 574
Pyrotechnic behavior 304, 467, 595
Radar attenuation 200, 206, 210
Ramjet 26-31, 106-109, 335, 351, 525, 526,
528, 535, 549, 579, 595, 601
Ramrocket 26-31, 335, 351, 539, 595, 601
RDX 42-46,125,487,504,507
Relaxation 67, 243, 244
Reliability 35, 37, 49, 75-78, 218, 362, 574,
592, 598, 600
Resonance rod 187
Reynolds number 161
Rolling 379, 383
Safety 49, 303, 345, 358, 410-412, 442, 449,
467, 495,519-523, 543
Safety coefficient, safety factor 65, 70, 71,
72, 74-77, 216, 288-297, 519
Safety margin 65, 77, 217
Screw extrusion 343, 377, 382, 390, 596
Secondary smoke 197, 212, 341, 512
Segmented grain 79, 80, 598
Service life 35, 40, 360, 363, 405, 406, 553,
571, 589, 592
Shear 233,443,454
Shell 349, 597
Shock sensitivity 386, 470, 521, 522
Signature 193, 194, 333, 341, 342, 399, 460,
511, 515, 530, 544, 549, 561, 572, 591
Space motors 79, 80, 597-600
Specific impulse 19, 21, 25, 27, 81, 85,
96-106, 332-333, 398, 426, 434, 460, 493,
510-512, 534, 538, 542, 545, 549, 586,
588, 589, 594, 595, 597
Spraying 566, 568
Stabilizer 317, 371, 375, 376, 405, 408, 488,
516
Stamping 343,381,448
Standard motor 11, 99, 116
Standard specific impulse 10, 54, 105, 106,
108
Static electricity 3 1 9, 4 1 1 , 47 1 -473, 523, 578
Steady state combustion 10, 93, 135
Steady state flow 91, 92
Strain 67, 70, 128, 217, 225-229, 237, 270,
276, 291,417, 501,502, 503, 592
Strand burner 113, 307
Stress 67, 70, 138, 217, 225-229, 237, 270,
276, 293, 417, 466, 501, 502, 503, 592
Structural analysis 36, 52, 53, 65, 74, 215
Structural integrity 52, 82, 216
Swelling 377, 380, 419, 571
T burner 181, 182
Tear 262
Temperature coefficient 14, 59, 112, 335,
372, 375, 395, 507, 539
Tensile test 71, 233-236, 240 242, 501
Terminology 47-48
Theoretical specific impulse 24, 96
Thermal conductivity 391, 554, 580
Thermal cycles 42, 48, 49, 295, 338-340,
501, 592, 601
Thermal expansion coefficient 340, 391,
417, 499, 580
Thermal explosion 307, 317
Thermal insulation 5, 6, 50, 454, 553, 554,
567, 590
Thermal protection 3, 44, 494, 549, 550,
558, 579
Thermal shrinkage 280
Thermoinitiation 317, 410, 470, 523
Thrust 1, 15, 17, 19, 30, 48, 52, 53, 79, 80,
416, 598
Thrust coefficient 18, 31, 89
Thrust law 13
Thrust measurement 97, 98
606
Index
Thrust modulation 592, 593, 594, 597
Thrust vector control 8
Time-temperature equivalence 246-249
TNT equivalency 308, 309
Total impulse 20, 48, 55, 75, 96, 550
Toxicity 586
Transverse instabilities 174, 185, 401, 513
Turbojet 594, 601
Turboramjet 595, 601
Unsteady combustion 140, 141, 164, 175
Value analysis 361, 362
Velocity coupling 175, 178, 183
Viscoelasticity 235, 251, 336, 417, 418
Viscosity 374, 380, 422, 431, 433, 442, 444,
451, 453, 495, 542, 568, 575, 578, 599
Volume change 241, 388, 503
Volumetric loading fraction 41, 55, 81, 549,
589
Vulnerability 49, 345, 488, 593, 595, 598,
601
XDT 311
Zirconium 336, 403, 533 535, 537, 551, 586
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